- Quantum electrodynamics
**Quantum electrodynamics**(**QED**) is a relativisticquantum field theory ofelectrodynamics . QED was developed by a number of physicists, beginning in the late 1920s. It basically describes how light and matter interact. More specifically it deals with the interactions between electrons,positrons and photons. QED mathematically describes all phenomena involving electrically charged particles interacting by means ofexchange ofphotons . It has been called "the jewel of physics" for its extremely accurate predictions of quantities like theanomalous magnetic moment of theelectron , and theLamb shift of theenergy level s ofhydrogen . []Richard Feynman , 1985. " [*http://www.amazon.com/gp/reader/0691024170 QED: The strange theory of light and matter*] " (chapter 1, page 6, first paragraph). Princeton Univ. Press.In technical terms, QED can be described as a perturbation theory of the

electromagnetic quantum vacuum.**History**The word 'quantum' is

Latin , meaning "how much" (neut. sing. of quantus "how great"). [] The word 'electrodynamics' was coined byOnline Etymology Dictionary André-Marie Ampère in 1822. [*Grandy, W.T. (2001). "Relativistic Quantum Mechanics of Leptons and Fields", Springer.*] The word 'quantum', as used in physics, i.e. with reference to the notion of count, was first used by Max Planck, in 1900 and reinforced by Einstein in 1905 with his use of the term "light quanta".Quantum theory began in 1900, when

Max Planck assumed that energy isquantized in order to derive a formula predicting the observed frequency dependence of the energy emitted by ablack body . This dependence is completely at variance withclassical physics . In 1905, Einstein explained thephotoelectric effect by postulating that light energy comes in quanta later calledphoton s. In 1913, Bohr invokedquantization in his proposed explanation of thespectral lines of thehydrogen atom. In 1924,Louis de Broglie proposed a quantum theory of the wave-like nature ofsubatomic particle s. 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.Modern

quantum mechanics was born in 1925 withWerner Heisenberg 'smatrix mechanics andErwin Schrödinger 'swave mechanics and theSchrödinger 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 hisuncertainty principle , and theCopenhagen interpretation of quantum mechanics began to take shape. Around this time,Paul Dirac , in work culminating in his 1930 monograph finally joined quantum mechanics andspecial relativity , pioneered the use ofoperator theory , and devised thebra-ket notation widely used since. In 1932,John von Neumann formulated the rigorous mathematical basis forquantum mechanics as the theory oflinear operator s onHilbert space s. This and other work from the founding period remains valid and widely used.Quantum chemistry began withWalter Heitler andFritz London 's 1927 quantum account of thecovalent bond of thehydrogen molecule .Linus Pauling and others contributed to the subsequent development of quantum chemistry.The application of quantum mechanics to fields rather than single particles, resulting in what are known as quantum field theories, began in 1927. Early contributors included Dirac,

Wolfgang Pauli , Weisskopf, and Jordan. This line of research culminated in the 1940s in the quantum electrodynamics (QED) ofRichard Feynman ,Freeman Dyson ,Julian Schwinger , andSin-Itiro Tomonaga , for which Feynman, Schwinger and Tomonaga received the1965 Nobel Prize in Physics . QED, a quantum theory ofelectron s,positron s, and theelectromagnetic field , was the first satisfactory quantum description of a physical field and of the creation and annihilation ofquantum particle s.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, butFreeman Dyson later showed that the two approaches were equivalent. Therenormalization procedure for eliminating the awkward infinite predictions ofquantum 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)QED has served as the 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 byH. David Politzer ,Sidney Coleman ,David Gross andFrank Wilczek . Building on the pioneering work ofSchwinger ,Peter Higgs , Goldstone, and others,Sheldon Glashow ,Steven Weinberg andAbdus Salam independently showed how theweak nuclear force and quantum electrodynamics could be merged into a singleelectroweak 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 anelectron or aproton ) passes over every possible path allowed byaperture s 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 atvelocity c on average [*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 textPhysically, QED describes charged particles (and their

antiparticle s) interacting with each other by the exchange ofphoton s. The magnitude of these interactions can be computed using perturbation theory; these rather complex formulas have a remarkable pictorial representation asFeynman diagram s. QED was the theory to which Feynman diagrams were first applied. These diagrams were invented on the basis ofLagrangian 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. The paths withstationary phase contribute most (due to lack ofdestructive interference with some neighboring counter-phase paths) — this results in the stationary classical path between the two points.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 seeprecision tests of QED . This makes QED one of the most accurate physical theories constructed thus far.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), , a classic non-mathematical exposition of QED from the point of view articulated above.**Mathematics**Mathematically, QED is an

abelian gauge theory with the symmetry groupU(1) . Thegauge field , which mediates the interaction between the charged spin-1/2 fields, is theelectromagnetic field .The QEDLagrangian for a spin-1/2 field interacting with the electromagnetic field is given by the real part of::$mathcal\{L\}=arpsi(igamma^mu\; D\_mu-m)psi\; -frac\{1\}\{4\}F\_\{mu\; u\}F^\{mu\; u\};,$

:where::$gamma\_mu\; ,!$ are

Dirac matrices ;::$psi$ abispinor field ofspin-1/2 particles (e.g.electron -positron field);::$arpsiequivpsi^daggergamma\_0$, called "psi-bar", is sometimes referred to asDirac adjoint ;::$D\_mu\; =\; partial\_mu+ieA\_mu\; ,!$ is the gaugecovariant derivative ;::$e$ is the coupling constant, equal to theelectric charge of the bispinor field; ::$A\_mu$ is thecovariant four-potential of the electromagnetic field;::$F\_\{mu\; u\}\; =\; partial\_mu\; A\_\; u\; -\; partial\_\; u\; A\_mu\; ,!$ is theelectromagnetic field tensor .**Euler-Lagrange equations**To begin, substituting the definition of "D" into the Lagrangian gives us:::$mathcal\{L\}\; =\; i\; ar\{psi\}\; gamma^mu\; partial\_mu\; psi\; -\; ear\{psi\}gamma\_mu\; A^mu\; psi\; -m\; ar\{psi\}\; psi\; -\; frac\{1\}\{4\}F\_\{mu\; u\}F^\{mu\; u\}.\; quad\; quad\; ,$

Next, we can substitute this Lagrangian into the

Euler-Lagrange equation of motion for a field:::$partial\_mu\; left(\; frac\{partial\; mathcal\{L\{partial\; (\; partial\_mu\; psi\; )\}\; ight)\; -\; frac\{partial\; mathcal\{L\{partial\; psi\}\; =\; 0\; quad\; quad\; quad\; quad\; quad\; (2)\; ,$to find the field equations for QED.The two terms from this Lagrangian are then:::$partial\_mu\; left(\; frac\{partial\; mathcal\{L\{partial\; (\; partial\_mu\; psi\; )\}\; ight)\; =\; partial\_mu\; left(\; i\; ar\{psi\}\; gamma^mu\; ight)\; ,$

::$frac\{partial\; mathcal\{L\{partial\; psi\}\; =\; -ear\{psi\}gamma\_mu\; A^mu\; -\; m\; ar\{psi\}.\; ,$

Substituting these two back into the Euler-Lagrange equation (2) results in:::$i\; partial\_mu\; ar\{psi\}\; gamma^mu\; +\; ear\{psi\}gamma\_mu\; A^mu\; +\; m\; ar\{psi\}\; =\; 0\; ,$with complex conjugate:::$i\; gamma^mu\; partial\_mu\; psi\; -\; e\; gamma\_mu\; A^mu\; psi\; -\; m\; psi\; =\; 0.\; ,$

Bringing the middle term to the right-hand side transforms this second equation into:::

**References****Further reading****Books***

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***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.

**External links*** [

*http://nobelprize.org/physics/laureates/1965/feynman-lecture.html Feynman's Nobel Prize lecture describing the evolution of QED and his role in it*]

* [*http://www.vega.org.uk/video/subseries/8 Feynman's New Zealand lectures on QED for non-physicists*]

* [*http://daarb.narod.ru/qed-eng.html On quantization of electromagnetic field*]

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