The field of physics that studies the interaction of electromagnetic radiation with electrically charged matter within the framework of relativity and quantum mechanics. It is the fundamental theory underlying all disciplines of science concerned with electromagnetism, such as atomic physics, chemistry, biology, the theory of bulk matter, and electromagnetic radiation.

Efforts to formulate quantum electrodynamics (QED) were initiated by P. A. M. Dirac, W. Heisenberg, and W. Pauli soon after quantum mechanics was established. The first step was to remedy the obvious shortcoming of quantum mechanics: that it applies only to the case where particle speeds are small compared with that of light, c. This led to Dirac's discovery of a relativistic wave equation, in which the wave function has four components and is multiplied by certain 4 × 4 matrices. His equation incorporates in a natural manner the observed electron-spin angular momentum, which implies that the electron is a tiny magnet. The strength of this magnet (magnetic moment) was predicted by Dirac and agreed with observation. A detailed prediction of the hydrogen spectrum was also in good agreement with experiment. See also Atomic structure and spectra; Electron spin; Matrix theory.

In order to go beyond this initial success and calculate higher-order effects, however, the interaction of charge and electromagnetic field had to be treated dynamically. To begin with, a good theoretical framework had to be found for describing the wave-particle duality of light, that is, the experimentally well-established fact that light behaves like a particle (photon) in some cases but like a wave in others. Similarly, the electron manifests wave-particle duality, another observed fact. Once this problem was settled, the next question was how to deal with the interaction of charge and electromagnetic field. It is here that the theory ran into severe difficulties. Its predictions often diverged when attempts were made to calculate beyond lowest-order approximations. This inhibited the further development of the theory for nearly 20 years. Stimulated by spectroscopic experiments vastly refined by microwave technology developed during World War II, however, S. Tomonaga, R. P. Feynman, and J. Schwinger discovered that the difficulties disappear if all observable quantities are expressed in terms of the experimentally measured charge and mass of the electron. With the discovery of this procedure, called renormalization, quantum electrodynamics became a theory in which all higher-order corrections are finite and well defined. See also Photon; Quantum mechanics; Relativistic quantum theory; Relativity; Wave mechanics.

Quantum electrodynamics is the first physical theory ever developed that has no obvious intrinsic limitation and describes physical quantities from first principles. Nature accommodates forces other than the electromagnetic force, such as those responsible for radioactive disintegration of heavy nuclei (called the weak force) and the force that binds the nucleus together (called the strong force). A theory called the standard model, has been developed which unifies the three forces and accounts for all experimental data from very low to extremely high energies. This does not mean, however, that quantum electrodynamics fails at high energies. It simply means that the real world has forces other than electromagnetism.

High-precision tests have provided excellent confirmation for the validity of the renormalization theory of quantum electrodynamics. In the high-energy regime, tests using electron-positron colliding-beam facilities at various high-energy physics laboratories have confirmed the predictions of quantum electrodynamics at center-of-mass energies up to 1.8 × 10¹¹ electronvolts (180 GeV). The uncertainty principle implies that this is equivalent to saying that quantum electrodynamics is valid down to about 10⁻¹⁷ meter, a distance 100 times shorter than the radius of the proton.

High-precision tests of quantum electrodynamics have also been carried out at low energies by using various simple atomic systems. The most accurate is that of the measurement of the magnetic moment of the electron, or the gyromagnetic ratio g, the ratio of spin and rotation frequencies, which is correctly predicted by quantum electrodynamics to 12 significant figures. This is the most precise confirmation of any theory ever carried out. See also Quantum field theory.

Britannica Concise Encyclopedia: quantum electrodynamics

Quantum theory of the interactions of charged particles with the electromagnetic field. It describes the interactions of light with matter as well as those of charged particles with each other. Its foundations were laid by P. A. M. Dirac when he discovered an equation describing the motion and spin of electrons that incorporated both quantum mechanics and the theory of special relativity. The theory, as refined and developed in the late 1940s, rests on the idea that charged particles interact by emitting and absorbing photons. It has become a model for other quantum field theories.

For more information on quantum electrodynamics, visit Britannica.com.

Columbia Encyclopedia: quantum electrodynamics

(QED), quantum field theory that describes the properties of electromagnetic radiation and its interaction with electrically charged matter in the framework of quantum theory. QED deals with processes involving the creation of elementary particles from electromagnetic energy, and with the reverse processes in which a particle and its antiparticle annihilate each other and produce energy. The fundamental equations of QED apply to the emission and absorption of light by atoms and the basic interactions of light with electrons and other elementary particles. Charged particles interact by emitting and absorbing photons, the particles of light that transmit electromagnetic forces. For this reason, QED is also known as the quantum theory of light.

QED is based on the elements of quantum mechanics laid down by such physicists as P. A. M. Dirac, W. Heisenberg, and W. Pauli during the 1920s, when photons were first postulated. In 1928 Dirac discovered an equation describing the motion of electrons that incorporated both the requirements of quantum theory and the theory of special relativity. During the 1930s, however, it became clear that QED as it was then postulated gave the wrong answers for some relatively elementary problems. For example, although QED correctly described the magnetic properties of the electron and its antiparticle, the positron, it proved difficult to calculate specific physical quantities such as the mass and charge of the particles. It was not until the late 1940s, when experiments conducted during World War II that had used microwave techniques stimulated further work, that these difficulties were resolved. Proceeding independently, Freeman J. Dyson, Richard P. Feynman and Julian S. Schwinger in the United States and Shinichiro Tomonaga in Japan refined and fully developed QED. They showed that two charged particles can interact in a series of processes of increasing complexity, and that each of these processes can be represented graphically through a diagramming technique developed by Feynman. Not only do these diagrams provide an intuitive picture of the process but they show how to precisely calculate the variables involved. The mathematical structures of QED later were adapted to the study of the strong interactions between quarks, which is called quantum chromodynamics.

Bibliography

See R. P. Feynman, QED (1985); P. W. Milonni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics (1994); S. S. Schweber, QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga (1994); G. Scharf, Finite Quantum Electrodynamics: The Causal Approach (1995).

Wikipedia: quantum electrodynamics

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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.

History

Main article: History of quantum mechanics

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.

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.

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.

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.

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) of Richard Feynman, Freeman Dyson, Julian Schwinger, and Sin-Itiro Tomonaga, for which Feynman, Schwinger and Tomonaga received the 1965 Nobel Prize in Physics. 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.

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)

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.

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].

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.

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.

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.

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

$\mathcal{L}=\bar\psi(i\gamma^\mu D_\mu-m)\psi -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}. \,$

where

$\gamma_\mu \,\!$ are Dirac matrices.

$\ \psi$ and its Dirac adjoint $\bar\psi$ 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

$F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu \,\!$ the electromagnetic field tensor.

Euler-Lagrange equations

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

$\mathcal{L} = i \bar{\psi} \gamma^\mu \partial_\mu \psi - e\bar{\psi}\gamma_\mu A^\mu \psi -m \bar{\psi} \psi - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}. \quad \quad (1) \,$

One can plug this Lagrangian into the Euler-Lagrange equation of motion for a field

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

to find the field equations for QED.

The two terms from this lagrangian are then

$\partial_\mu \left( \frac{\partial \mathcal{L}}{\partial ( \partial_\mu \psi )} \right) = \partial_\mu \left( i \bar{\psi} \gamma^\mu \right) \,$

$\frac{\partial \mathcal{L}}{\partial \psi} = -e\bar{\psi}\gamma_\mu A^\mu - m \bar{\psi} \,$

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

$i \partial_\mu \bar{\psi} \gamma^\mu + e\bar{\psi}\gamma_\mu A^\mu + m \bar{\psi} = 0 \,$

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.

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

$\partial_\nu \left( \frac{\partial \mathcal{L}}{\partial ( \partial_\nu A_\mu )} \right) - \frac{\partial \mathcal{L}}{\partial A_\mu} = 0 . \quad \quad \quad (3) \,$

The two terms this time are

$\partial_\nu \left( \frac{\partial \mathcal{L}}{\partial ( \partial_\nu A_\mu )} \right) = \partial_\nu \left( \partial^\mu A^\nu - \partial^\nu A^\mu \right) \,$

$\frac{\partial \mathcal{L}}{\partial A_\mu} = -e\bar{\psi} \gamma^\mu \psi \,$

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.

The one-loop contribution to the vacuum polarization function

The one-loop contribution to the electron self-energy function

The one-loop contribution to the vertex function

References

External links

Quantum Electrodynamics
electron • positron • photon • self-energy • vacuum polarization • vertex function • Gupta-Bleuler formalism • ξ gauge • Ward-Takahashi identity • Compton scattering • Bhabha scattering • Møller scattering • anomalous magnetic dipole moment • bremsstrahlung • positronium

General subfields within physics
Classical mechanics · Electromagnetism · Thermodynamics · Statistical mechanics · Quantum mechanics · Relativity · High energy physics · Condensed matter physics · Atomic, molecular, and optical physics

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		Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2007. Published by Houghton Mifflin Company. All rights reserved. Read more
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quantum electrodynamics

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