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Encyclopedia > Quantum electrodynamics
 Quantum physics $Delta x , Delta p ge frac{hbar}{2}$ Quantum mechanics Introduction to... Mathematical formulation of... Fig. ... Quantum mechanics (QM, or quantum theory) is a physical science dealing with the behaviour of matter and energy on the scale of atoms and subatomic particles / waves. ... The mathematical formulation of quantum mechanics is the body of mathematical formalisms which permits a rigorous description of quantum mechanics. ... Fundamental concepts Decoherence · Interference Uncertainty · Exclusion Transformation theory Ehrenfest theorem · Measurement Superposition · Entanglement In quantum mechanics, quantum decoherence is the mechanism by which quantum systems interact with their environments to exhibit probabilistically additive behavior - a feature of classical physics - and give the appearance of wavefunction collapse. ... Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ... In quantum physics, the outcome of even an ideal measurement of a system is not deterministic, but instead is characterized by a probability distribution, and the larger the associated standard deviation is, the more uncertain we might say that that characteristic is for the system. ... The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. ... The term transformation theory refers to a procedure used by P. A. M. Dirac in his early formulation of quantum theory, from around 1927. ... The Ehrenfest theorem, named after Paul Ehrenfest, relates the time derivative of the expectation value for a quantum mechanical operator to the commutator of that operator with the Hamiltonian of the system. ... The framework of quantum mechanics requires a careful definition of measurement, and a thorough discussion of its practical and philosophical implications. ... Quantum superposition is the application of the superposition principle to quantum mechanics. ... It has been suggested that Quantum coherence be merged into this article or section. ... Experiments Double-slit experiment Davisson-Germer experiment Stern–Gerlach experiment Bell's inequality experiment Popper's experiment Schrödinger's cat Double-slit diffraction and interference pattern The double-slit experiment consists of letting light diffract through two slits, which produces fringes or wave-like interference patterns on a screen. ... In 1927 at Bell Labs, Clinton Davisson and Lester Germer fired slow moving electrons at a crystalline Nickel target. ... In quantum mechanics, the Sternâ€“Gerlach experiment, named after Otto Stern and Walther Gerlach, is a celebrated experiment in 1920 on deflection of particles, often used to illustrate basic principles of quantum mechanics. ... In quantum mechanics, Bells Theorem states that a Bell inequality must be obeyed under any local hidden variable theory but can in certain circumstances be violated under quantum mechanics (QM). ... Poppers experiment is an experiment proposed by the 20th century philosopher of science Karl Popper, to test the standard interpretation (the Copenhagen interpretation) of Quantum mechanics. ... SchrÃ¶dingers Cat: When the nucleus (bottom left) decays, the Geiger counter (bottom centre) may sense it and trigger the release of the gas. ... Equations Schrödinger equation Pauli equation Klein-Gordon equation Dirac equation For a non-technical introduction to the topic, please see Introduction to quantum mechanics. ... The Pauli equation is a SchrÃ¶dinger equation which handles spin. ... The Klein-Gordon equation (Klein-Fock-Gordon equation or sometimes Klein-Gordon-Fock equation) is the relativistic version of the SchrÃ¶dinger equation. ... In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary spin-Â½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ... Advanced theories Quantum field theory Wightman axioms Quantum electrodynamics Quantum chromodynamics Quantum gravity Feynman diagram Quantum field theory (QFT) is the quantum theory of fields. ... In physics the Wightman axioms are an attempt of mathematically stringent, axiomatic formulation of quantum field theory. ... Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). ... This article does not cite any references or sources. ... In this Feynman diagram, an electron and positron annihilate and become a quark-antiquark pair. ... Interpretations Copenhagen · Ensemble Hidden variables · Transactional Many-worlds · Consistent histories Quantum logic Consciousness causes collapse It has been suggested that Quantum mechanics, philosophy and controversy be merged into this article or section. ... The Copenhagen interpretation is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. ... The Ensemble Interpretation, or Statistical Interpretation of Quantum Mechanics, is an interpretation that can be viewed as a minimalist interpretation. ... In physics, a hidden variable theory is urged by a minority of physicists who argue that the statistical nature of quantum mechanics implies that quantum mechanics is incomplete; it is really applicable only to ensembles of particles; new physical phenomena beyond quantum mechanics are needed to explain an individual event. ... The transactional interpretation of quantum mechanics (TIQM) by Professor John Cramer is an unusual interpretation of quantum mechanics that describes quantum interactions in terms of a standing wave formed by retarded (forward in time) and advanced (backward in time) waves. ... The many-worlds interpretation or MWI (also known as relative state formulation, theory of the universal wavefunction, many-universes interpretation, Oxford interpretation or many worlds), is an interpretation of quantum mechanics that claims to resolve all the paradoxes of quantum theory by allowing every possible outcome to every event to... In quantum mechanics, the consistent histories approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology. ... In mathematical physics and quantum mechanics, quantum logic can be regarded as a kind of propositional logic suitable for understanding the apparent anomalies regarding quantum measurement, most notably those concerning composition of measurement operations of complementary variables. ... Consciousness causes collapse is the theory that observation by a conscious observer is responsible for the wavefunction collapse in quantum mechanics. ... Scientists Planck · Schrödinger Heisenberg · Bohr · Pauli Dirac · Bohm · Born de Broglie · von Neumann Einstein · Feynman Everett · Others â€œPlanckâ€ redirects here. ... Bust of SchrÃ¶dinger, in the courtyard arcade of the main building, University of Vienna, Austria. ... Werner Karl Heisenberg (December 5, 1901 â€“ February 1, 1976) was a celebrated German physicist and Nobel laureate, one of the founders of quantum mechanics and acknowledged to be one of the most important physicists of the twentieth century. ... Niels (Henrik David) Bohr (October 7, 1885 â€“ November 18, 1962) was a Danish physicist who made fundamental contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in 1922. ... This article is about Austrian-Swiss physicist Wolfgang Pauli. ... Paul Adrien Maurice Dirac, OM, FRS (IPA: [dÉªrÃ¦k]) (August 8, 1902 â€“ October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ... David Bohm. ... Max Born (December 11, 1882 in Breslau â€“ January 5, 1970 in GÃ¶ttingen) was a mathematician and physicist. ... Louis-Victor-Pierre-Raymond, 7th duc de Broglie, generally known as Louis de Broglie (August 15, 1892â€“March 19, 1987), was a French physicist and Nobel Prize laureate. ... For other persons named John Neumann, see John Neumann (disambiguation). ... â€œEinsteinâ€ redirects here. ... This article is about the physicist. ... Hugh Everett III (November 11, 1930 â€“ July 19, 1982) was an American physicist who first proposed the many-worlds interpretation(MWI) of quantum physics, which he called his relative state formulation. ... Below is a list of famous physicists. ... This box: view • talk • edit

Quantum electrodynamics (QED) is a relativistic quantum field theory of electrodynamics. QED was developed by a number of physicists, beginning in the late 1920s.[1] QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons. It has been called "the jewel of physics" for its extremely accurate predictions of quantities like the anomalous magnetic moment of the electron, and the Lamb shift of the energy levels of hydrogen. Quantum field theory (QFT) is the quantum theory of fields. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ... For other uses, see Phenomena (disambiguation). ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... Look up exchange in Wiktionary, the free dictionary. ... In physics, the photon (from Greek Ï†Ï‰Ï‚, phÅs, meaning light) is the quantum of the electromagnetic field; for instance, light. ... Quantum electrodynamics (QED) is the most stringently tested theory in physics (after special relativity which currently is tested to 10-15). ... In quantum electrodynamics, anomalous magnetic moment of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle. ... For other uses, see Electron (disambiguation). ... In physics, the Lamb shift, named after Willis Lamb, is a small difference in energy between two energy levels and of the hydrogen atom in quantum mechanics. ... A quantum mechanical system can only be in certain states, so that only certain energy levels are possible. ... General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ...

## Contents

The word 'quantum' is Latin, meaning "how much," (neut. sing. of quantus "how great").[2] The word 'electrodynamics' was coined by André-Marie Ampère in 1822.[3] The word 'quantum', as used in physics, was first used by Max Planck, i.e. "energy elements", in 1900 and reinforced by Einstein in 1905 with his use of the term light quanta. Niels Bohrâ€™s 1913 quantum model of the atom, which incorporated an explanation of Johannes Rydbergs 1888 formula, Max Planckâ€™s 1900 quantum hypothesis, i. ... For other uses, see Latin (disambiguation). ... AndrÃ©-Marie AmpÃ¨re (January 20, 1775 â€“ June 10, 1836), was a French physicist who is generally credited as one of the main discoverers of electromagnetism. ...

Quantum theory began in 1900, when Max Planck assumed that energy is quantized in order to derive a formula predicting the observed frequency dependence of the energy emitted by a black body. This dependence is completely at variance with classical physics. In 1905, Einstein explained the photoelectric effect by postulating that light energy comes in quanta later called photons. In 1913, Bohr invoked quantization in his proposed explanation of the spectral lines of the hydrogen atom. In 1924, Louis de Broglie proposed a quantum theory of the wave-like nature of subatomic particles. The phrase "quantum physics" was first employed in Johnston's Planck's Universe in Light of Modern Physics. These theories, while they fit the experimental facts to some extent, were strictly phenomenological: they provided no rigorous justification for the quantization they employed. â€œPlanckâ€ redirects here. ... Generally, quantization is the state of being constrained to a set of discrete values, rather than varying continuously. ... As the temperature decreases, the peak of the black body radiation curve moves to lower intensities and longer wavelengths. ... Classical physics is physics based on principles developed before the rise of quantum theory, usually including the special theory of relativity and general theory of relativity. ... â€œEinsteinâ€ redirects here. ... A diagram illustrating the emission of electrons from a metal plate, requiring energy gained from an incoming photon to be more than the work function of the material. ... In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ... Niels (Henrik David) Bohr (October 7, 1885 â€“ November 18, 1962) was a Danish physicist who made fundamental contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in 1922. ... Look up quantization in Wiktionary, the free dictionary. ... A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from an excess or deficiency of photons in a narrow frequency range, compared with the nearby frequencies. ... General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ... Louis-Victor-Pierre-Raymond, 7th duc de Broglie, generally known as Louis de Broglie (August 15, 1892â€“March 19, 1987), was a French physicist and Nobel Prize laureate. ... Helium atom (schematic) Showing two protons (red), two neutrons (green) and two electrons (yellow). ...

Modern quantum mechanics was born in 1925 with Werner Heisenberg's matrix mechanics and Erwin Schrödinger's wave mechanics and the Schrödinger equation, which was a non-relativistic generalization of de Broglie's(1925) relativistic approach. Schrödinger subsequently showed that these two approaches were equivalent. In 1927, Heisenberg formulated his uncertainty principle, and the Copenhagen interpretation of quantum mechanics began to take shape. Around this time, Paul Dirac, in work culminating in his 1930 monograph finally joined quantum mechanics and special relativity, pioneered the use of operator theory, and devised the bra-ket notation widely used since. In 1932, John von Neumann formulated the rigorous mathematical basis for quantum mechanics as the theory of linear operators on Hilbert spaces. This and other work from the founding period remains valid and widely used. Fig. ... Werner Karl Heisenberg (December 5, 1901 â€“ February 1, 1976) was a celebrated German physicist and Nobel laureate, one of the founders of quantum mechanics and acknowledged to be one of the most important physicists of the twentieth century. ... Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. ... Bust of SchrÃ¶dinger, in the courtyard arcade of the main building, University of Vienna, Austria. ... The wave equation is an important partial differential equation which generally describes all kinds of waves, such as sound waves, light waves and water waves. ... For a non-technical introduction to the topic, please see Introduction to quantum mechanics. ... In quantum physics, the outcome of even an ideal measurement of a system is not deterministic, but instead is characterized by a probability distribution, and the larger the associated standard deviation is, the more uncertain we might say that that characteristic is for the system. ... The Copenhagen interpretation is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. ... Paul Adrien Maurice Dirac, OM, FRS (IPA: [dÉªrÃ¦k]) (August 8, 1902 â€“ October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ... For a less technical and generally accessible introduction to the topic, see Introduction to special relativity. ... In mathematics, operator theory is the branch of functional analysis which deals with bounded linear operators and their properties. ... Bra-ket notation is the standard notation for describing quantum states in the theory of quantum mechanics. ... For other persons named John Neumann, see John Neumann (disambiguation). ... Fig. ... In mathematics, a linear transformation (also called linear operator or linear map) is a function between two vector spaces that respects the arithmetical operations addition and scalar multiplication defined on vector spaces, or, in other words, it preserves linear combinations. Definition and first consequences Formally, if V and W are... The mathematical concept of a Hilbert space (named after the German mathematician David Hilbert) generalizes the notion of Euclidean space in a way that extends methods of vector algebra from the plane and three-dimensional space to spaces of functions. ...

Quantum chemistry began with Walter Heitler and Fritz London's 1927 quantum account of the covalent bond of the hydrogen molecule. Linus Pauling and others contributed to the subsequent development of quantum chemistry. Quantum chemistry is a branch of theoretical chemistry, which applies quantum mechanics and quantum field theory to address issues and problems in chemistry. ... Walter Heinrich Heitler (02. ... Fritz Wolfgang London (March 7, 1900â€“March 30, 1954) was a German-born American physicist for whom the London force is named. ... â€œCovalentâ€ redirects here. ... General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ... 3D (left and center) and 2D (right) representations of the terpenoid molecule atisane. ... Linus Carl Pauling (February 28, 1901 â€“ August 19, 1994) was an American quantum chemist and biochemist. ...

QED involves a covariant and gauge invariant prescription for the calculation of observable quantities. Feynman's mathematical technique, based on his diagrams, initially seemed very different from the field-theoretic, operator-based approach of Schwinger and Tomonaga, but Freeman Dyson later showed that the two approaches were equivalent. The renormalization procedure for eliminating the awkward infinite predictions of quantum field theory was first implemented in QED. Even though renormalization works very well in practice, Feynman was never entirely comfortable with its mathematical validity, even referring to renormalization as a "shell game" and "hocus pocus". (Feynman, 1985: 128) In category theory, see covariant functor. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In this Feynman diagram, an electron and positron annihilate and become a quark-antiquark pair. ... In mathematics, an operator is a function that performs some sort of operation on a number, variable, or function. ... Freeman John Dyson FRS (born December 15, 1923) is an English-born American theoretical physicist and mathematician, famous for his work in quantum mechanics, solid-state physics, nuclear weapons design and policy, and for his serious theorizing in futurism and science fiction concepts, including the search for extraterrestrial intelligence. ... Figure 1. ... Quantum field theory (QFT) is the quantum theory of fields. ...

QED has served as a role model and template for all subsequent quantum field theories. One such subsequent theory is quantum chromodynamics, which began in the early 1960s and attained its present form in the 1975 work by H. David Politzer, Sidney Coleman, David Gross and Frank Wilczek. Building on the pioneering work of Schwinger, Peter Higgs, Goldstone, and others, Sheldon Glashow, Steven Weinberg and Abdus Salam independently showed how the weak nuclear force and quantum electrodynamics could be merged into a single electroweak force. Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). ... Prof. ... Sidney Coleman at Harvard University Sidney Coleman is an eminent theoretical physicist. ... David Jonathan Gross (born February 19, 1941 in Washington, D.C.) is an American particle physicist and string theorist (although hes stated to the Brazilian newspaper Folha de SÃ£o Paulo, on 09/27/2006, that the second area is included in the first one). ... Frank Wilczek (born May 15, 1951) is a Nobel prize winning American physicist. ... Julian Seymour Schwinger (February 12, 1918 -- July 16, 1994) was an American theoretical physicist. ... Peter Ware Higgs (born May 29, 1929), FRSE, FRS, until recently held a personal chair in theoretical physics at the University of Edinburgh and is now an emeritus professor. ... Professor Sheldon Lee Glashow (born December 5, 1932) is an American physicist. ... Steven Weinberg (born May 3, 1933) is an American physicist. ... For other uses, see Abdus Salam (disambiguation). ... The weak nuclear force or weak interaction is one of the four fundamental forces of nature. ... In physics, the electroweak theory presents a unified description of two of the four fundamental forces of nature: electromagnetism and the weak nuclear force. ...

## Physical interpretation of QED

In classical optics light travels over all allowed paths, and their interference results in Fermat's principle. Similarly, in QED light (or any other particle like an electron or a proton) passes over every possible path allowed by apertures or lenses. The observer (at a particular location) simply detects the mathematical result of all wave functions added up, as a sum of all line integrals. For other interpretations, paths are viewed as non physical, mathematical constructs that are equivalent to other, possibly infinite, sets of mathematical expansions. According to QED, light can go slower or faster than c, but will travel at speed c on average[4]. Fermats principle assures that the angles given by Snells law always reflect lights quickest path between P and Q. Fermats principle in optics states: This principle was first stated by Pierre de Fermat. ... For other uses, see Electron (disambiguation). ... In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... a big (1) and a small (2) aperture For other uses, see Aperture (disambiguation). ... A lens is: a part of the eye an optical device that may be used in a camera or in a telescope; see lens (optics). ... In mathematics, a set can be thought of as any collection of distinct objects considered as a whole. ... â€œLightspeedâ€ redirects here. ...

Physically, QED describes charged particles (and their antiparticles) interacting with each other by the exchange of photons. The magnitude of these interactions can be computed using perturbation theory; these rather complex formulas have a remarkable pictorial representation as Feynman diagrams [1]. QED was the theory to which Feynman diagrams were first applied. These diagrams were invented on the basis of Lagrangian mechanics. Using a Feynman diagram, one decides every possible path between the start and end points. Each path is assigned a complex-valued probability amplitude, and the actual amplitude we observe is the sum of all amplitudes over all possible paths. Obviously, among all possible paths the ones with stationary phase contribute most (due to lack of destructive interference with some neighboring counter-phase paths) — this results in the stationary classical path between the two points. Corresponding to most kinds of particle, there is an associated antiparticle with the same mass and opposite charges. ... In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ... In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. ... In this Feynman diagram, an electron and positron annihilate and become a quark-antiquark pair. ... Lagrangian mechanics is a re-formulation of classical mechanics that combines conservation of momentum with conservation of energy. ... In mathematics, a complex number is a number of the form where a and b are real numbers, and i is the imaginary unit, with the property i 2 = âˆ’1. ... Stationary can mean: Look up stationary in Wiktionary, the free dictionary. ... Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ...

QED doesn't predict what will happen in an experiment, but it can predict the probability of what will happen in an experiment, which is how it is experimentally verified. Predictions of QED agree with experiments to an extremely high degree of accuracy: currently about 10−12 (and limited by experimental errors); for details see precision tests of QED. This makes QED the most accurate physical theory constructed thus far. Quantum electrodynamics (QED) is the most stringently tested theory in physics (after special relativity which currently is tested to 10-15). ...

Near the end of his life, Richard P. Feynman gave a series of lectures on QED intended for the lay public. These lectures were transcribed and published as Feynman (1985), QED: The strange theory of light and matter, a classic non-mathematical exposition of QED from the point of view articulated above. Richard Feynman Richard Phillips Feynman (May 11, 1918&#8211;February 15, 1988) (surname pronounced FINE-man) was one of the most influential American physicists of the 20th century, expanding greatly the theory of quantum electrodynamics. ... QED: The Strange Theory of Light and Matter (Alix G. Mautner Memorial Lectures) is a book by Richard Feynman consisting of four lectures which describe, for the general reader, quantum electrodynamics. ...

## Mathematics

Mathematically, QED has the structure of an abelian gauge theory with a symmetry group being U(1) gauge group. The gauge field which mediates the interaction between the charged spin-1/2 fields is the electromagnetic field. The QED Lagrangian for the interaction of electrons and positrons through photons is Abelian, in mathematics, is used in many different definitions: In group theory: Abelian group, a group in which the binary operation is commutative Category of abelian groups Ab has abelian groups as objects and group homomorphisms as morphisms Metabelian group is a group where the commutator subgroup is contained in... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In mathematics, the unitary group of degree n, denoted U(n), is the group of nÃ—n unitary matrices, with the group operation that of matrix multiplication. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ... The magnitude of an electric field surrounding two equally charged (repelling) particles. ... The electromagnetic field is a physical field that is produced by electrically charged objects and which affects the behaviour of charged objects in the vicinity of the field. ... A Lagrangian of a dynamical system, named after Joseph Louis Lagrange, is a function of the dynamical variables and concisely describes the equations of motion of the system. ... For other uses, see Electron (disambiguation). ... The first detection of the positron in 1932 by Carl D. Anderson The positron is the antiparticle or the antimatter counterpart of the electron. ... In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ...

$mathcal{L}=barpsi(igamma^mu D_mu-m)psi -frac{1}{4}F_{munu}F^{munu}. ,$
where
$gamma_mu ,!$ are Dirac matrices.
$psi$ and its Dirac adjoint $barpsi$ are the fields representing electrically charged particles, specifically electron and positron fields represented as Dirac spinors.
$D_mu = partial_mu+ieA_mu ,!$ is the gauge covariant derivative, with $e$ the coupling strength (equal to the elementary charge),
$A_mu$ the covariant vector potential of the electromagnetic field and
$F_{munu} = partial_mu A_nu - partial_nu A_mu ,!$ the electromagnetic field tensor.

The Dirac equation is a relativistic quantum mechanical wave equation invented by Paul Dirac in 1928. ... The Dirac adjoint of a Dirac spinor is defined to be the dual spinor , where denotes the time-like Dirac matrix. ... The magnitude of an electric field surrounding two equally charged (repelling) particles. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... For other uses, see Electron (disambiguation). ... The first detection of the positron in 1932 by Carl D. Anderson The positron is the antiparticle or the antimatter counterpart of the electron. ... In mathematics and physics, in particular in the theory of the orthogonal groups, spinors are certain kinds of mathematical objects (group representations of Spin(N), roughly speaking) similar to vectors, but which change sign under a rotation of radians. ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In category theory, see covariant functor. ... For a non-technical overview of the subject, see Calculus. ... The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. ... In category theory, see covariant functor. ... In vector calculus, a vector potential is a vector field whose curl is a given vector field. ... The electromagnetic field is a physical field that is produced by electrically charged objects and which affects the behaviour of charged objects in the vicinity of the field. ... In electromagnetism, the electromagnetic tensor, or electromagnetic field tensor, F, is defined as: where Ai is the vector potential. ...

### Euler-Lagrange equations

To begin, plug in the definition of D into the Lagrangian to see that L is

$mathcal{L} = i bar{psi} gamma^mu partial_mu psi - ebar{psi}gamma_mu A^mu psi -m bar{psi} psi - frac{1}{4}F_{munu}F^{munu}. quad quad (1) ,$

One can plug this Lagrangian into the Euler-Lagrange equation of motion for a field The Euler-Lagrange equation, developed by Leonhard Euler and Joseph-Louis Lagrange in the 1750s, is the major formula of the calculus of variations. ...

$partial_mu left( frac{partial mathcal{L}}{partial ( partial_mu psi )} right) - frac{partial mathcal{L}}{partial psi} = 0 . quad quad quad quad quad (2) ,$

to find the field equations for QED.

The two terms from this lagrangian are then

$partial_mu left( frac{partial mathcal{L}}{partial ( partial_mu psi )} right) = partial_mu left( i bar{psi} gamma^mu right) ,$
$frac{partial mathcal{L}}{partial psi} = -ebar{psi}gamma_mu A^mu - m bar{psi} ,$

Plugging these two back into the Euler-Lagrange equation (2) results in

$i partial_mu bar{psi} gamma^mu + ebar{psi}gamma_mu A^mu + m bar{psi} = 0 ,$

and the complex conjugate

$i gamma^mu partial_mu psi - e gamma_mu A^mu psi - m psi = 0. ,$

If you bring the middle term to the right-hand side looks like:

 $i gamma^mu partial_mu psi - m psi = e gamma_mu A^mu psi ,$

The left hand side is like the original Dirac equation and the right hand side is the interaction with the electromagnetic field. In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary spin-Â½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ...

One more important equation can be found by plugging in the lagrangian into one more Euler-lagrange equation, but now for the field, Aμ:

$partial_nu left( frac{partial mathcal{L}}{partial ( partial_nu A_mu )} right) - frac{partial mathcal{L}}{partial A_mu} = 0 . quad quad quad (3) ,$

The two terms this time are

$partial_nu left( frac{partial mathcal{L}}{partial ( partial_nu A_mu )} right) = partial_nu left( partial^mu A^nu - partial^nu A^mu right) ,$
$frac{partial mathcal{L}}{partial A_mu} = -ebar{psi} gamma^mu psi ,$

And these two terms, when plugged back into (3) give

 $partial_nu F^{nu mu} = e bar{psi} gamma^mu psi ,$

### In pictures

The part of the Lagrangian containing the electromagnetic field tensor describes the free evolution of the electromagnetic field, whereas the Dirac-like equation with the gauge covariant derivative describes the free evolution of the electron and positron fields as well as their interaction with the electromagnetic field. In electromagnetism, Maxwells equations are a set of equations first presented as a distinct group in the later half of the nineteenth century by James Clerk Maxwell. ... The electromagnetic field is a physical field that is produced by electrically charged objects and which affects the behaviour of charged objects in the vicinity of the field. ... In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary spin-Â½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In category theory, see covariant functor. ... For a non-technical overview of the subject, see Calculus. ... For other uses, see Electron (disambiguation). ... The first detection of the positron in 1932 by Carl D. Anderson The positron is the antiparticle or the antimatter counterpart of the electron. ... The electromagnetic field is a physical field that is produced by electrically charged objects and which affects the behaviour of charged objects in the vicinity of the field. ...

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 Abraham-Lorentz force Anomalous magnetic moment Basics of quantum mechanics Bhabha scattering Cavity quantum electrodynamics (Cavity QED) Compton scattering Gauge theory Gupta-Bleuler formalism Lamb shift Landau pole Moeller scattering Photon dynamics in the double-slit experiment Photon polarization Positronium Quantum chromodynamics Quantum field theory Quantum gauge theory Renormalization Scalar electrodynamics Schrödinger equation Schwinger model Schwinger-Dyson equation Self-energy Standard Model Theoretical and experimental justification for the Schrödinger equation Vacuum polarization Vertex function

Image File history File links Portal. ... The Abraham-Lorentz force is the average force on an accelerating charged particle caused by the particle emitting electromagnetic radiation. ... In quantum electrodynamics, anomalous magnetic moment of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle. ... Quantum mechanics is a physical science dealing with the behaviour of matter and waves on the scale of atoms and subatomic particles. ... In quantum electrodynamics, Bhabha scattering is the electron positron scattering process represented by . ... In physics, Compton scattering or the Compton effect, is the decrease in energy (increase in wavelength) of an X-ray or gamma ray photon, when it interacts with matter. ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In quantum field theory, the Gupta-Bleuler formalism is a way of quantizing the electromagnetic field. ... In physics, the Lamb shift, named after Willis Lamb, is a small difference in energy between two energy levels and of the hydrogen atom in quantum mechanics. ... In physics, Landau pole is the energy scale (or the precise value of the energy) where a coupling constant (the strength of an interaction) of a quantum field theory becomes infinite. ... MÃ¸ller scattering is the name given to electron-electron scattering in Quantum Field Theory. ... The Dynamics of photons in the double-slit experiment describes the relationship between classical electromagnetic waves and photons, the quantum counterpart of classical electromagnetic waves, in the context of the double-slit experiment. ... Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. ... Positronium (Ps) is a system consisting of an electron and its anti-particle, a positron, bound together into an exotic atom. The orbit of the two particles and the set of energy levels is similar to that of the hydrogen atom (electron and proton). ... Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). ... Quantum field theory (QFT) is the quantum theory of fields. ... See gauge theory for the classical prelimanaries. ... Figure 1. ... In theoretical physics, scalar electrodynamics is a theory of a U(1) gauge field coupled to a charged spin 0 scalar field that takes the place of the Dirac fermions in ordinary quantum electrodynamics. ... For a non-technical introduction to the topic, please see Introduction to quantum mechanics. ... In physics, the Schwinger model, named after Julian Schwinger, is the model describing 2D (2 spatial 1 time) Euclidean quantum electrodynamics with a Dirac fermion. ... The Schwinger-Dyson equation, named after Julian Schwinger and Freeman Dyson, is an equation of quantum field theory (QFT). ... In theoretical physics, a particles self-energy represents the contribution to the particles energy or effective mass due to interactions between the particle and the system it is apart of. ... The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ... The theoretical and experimental justification for the SchrÃ¶dinger equation motivates the discovery of the SchrÃ¶dinger equation, the equation that describes the dynamics of nonrelativistic particles. ... In quantum physics, if we expand about the Fock vacuum, the true vacuum contains short-lived virtual particle-antiparticle pairs which are created in pairs out of the Fock vacuum and then annihilate each other. ... In quantum electrodynamics, the vertex function is the one particle irreducible correlation function involving &#968;, and the vector potential A. It is unfortunate that the effective action &#915;eff and the vertex function &#915;&#956; happen to be described by the same letter. ...

## References

1. ^ Richard Feynman, 1985. QED: The strange theory of light and matter (chapter 1, page 6, first paragraph). Princeton Univ. Press.
2. ^ Online Etymology Dictionary
3. ^ Grandy, W.T. (2001). Relativistic Quantum Mechanics of Leptons and Fields, Springer.
4. ^ Richard P. Feynman QED:(QED (book)) p89-90 "the light has an amplitude to go faster or slower than the speed c, but these amplitudes cancel each other out over long distances"; see also accompanying text

This article is about the physicist. ... An editor has expressed a concern that the subject of the article does not satisfy the notability guideline for Web content. ... QED: The Strange Theory of Light and Matter (Alix G. Mautner Memorial Lectures) is a book by Richard Feynman consisting of four lectures which describe, for the general reader, quantum electrodynamics. ...

### Books

• Feynman, Richard Phillips (1998). Quantum Electrodynamics. Westview Press; New Ed edition. ISBN 978-0201360752.
• Tannoudji-Cohen, Claude; Dupont-Roc, Jacques, and Grynberg, Gilbert (1997). Photons and Atoms: Introduction to Quantum Electrodynamics. Wiley-Interscience. ISBN 978-0471184331.
• De Broglie, Louis (1925). Recherches sur la theorie des quanta [Research on quantum theory]. France: Wiley-Interscience.
• Jauch, J.M.; Rohrlich, F. (1980). The Theory of Photons and Electrons. Springer-Verlag. ISBN 978-0387072951.
• Miller, Arthur I. (1995). Early Quantum Electrodynamics : A Sourcebook. Cambridge University Press. ISBN 978-0521568913.
• Schweber, Silvian,S. (1994). QED and the Men Who Made It. Princeton University Press. ISBN 978-0691033273.
• Schwinger, Julian (1958). Selected Papers on Quantum Electrodynamics. Dover Publications. ISBN 978-0486604442.
• Greiner, Walter; Bromley, D.A.,Müller, Berndt. (2000). Gauge Theory of Weak Interactions. Springer. ISBN 978-3540676720.
• Kane, Gordon, L. (1993). Modern Elementary Particle Physics. Westview Press. ISBN 978-0201624601.

This article is about the physicist. ... Louis-Victor-Pierre-Raymond, 7th duc de Broglie, generally known as Louis de Broglie (August 15, 1892â€“March 19, 1987), was a French physicist and Nobel Prize laureate. ... Julian Seymour Schwinger (February 12, 1918 -- July 16, 1994) was an American theoretical physicist. ...

### Journals

• J.M. Dudley and A.M. Kwan, "Richard Feynman's popular lectures on quantum electrodynamics: The 1979 Robb Lectures at Auckland University," American Journal of Physics Vol. 64 (June 1996) 694-698.

Results from FactBites:

 Quantum electrodynamics Summary (6252 words) Quantum theory began in 1900, when Max Planck assumed that energy is quantized in order to derive a formula predicting the observed frequency dependence of the energy emitted by a fl body. Modern quantum mechanics was born in 1925 with Werner Heisenberg's matrix mechanics and Erwin Schrödinger's wave mechanics and the Schrödinger equation. QED, a quantum theory of electrons, positrons, and the electromagnetic field, was the first satisfactory quantum description of a physical field and of the creation and annihilation of quantum particles.
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