A modern theory of electromagnetic interactions, developed by US physicists Richard Feynman and Julian Schwinger (191894), Japanese physicist Sinichiro Tomonaga (190679), and others during the 1940s; also called QED. Charged subatomic particles interact via photons, the quantum of electromagnetic radiation. The theory predicts the electron g-factor and atomic energy levels to high precision. It is a prototype gauge theory on which theories of nuclear forces are modelled.
Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange by photons, whether the interaction is between light and matter or between two charged particles.
Physical interpretation of QED
In classical physics, due to interference, light is observed to take the stationary path between two points;
Physically, QED describes charged particles (and their antiparticles) interacting with each other by the exchange of photons.
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.
Near the end of his life, Richard P.
History
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. In 1924, Louis de Broglie proposed a quantum theory of the wave-like nature of subatomic particles.
Modern quantum mechanics was born in 1925 with Werner Heisenberg's matrix mechanics and Erwin Schrödinger's wave mechanics and the Schrödinger equation. 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, 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.
Quantum chemistry began with Walter Heitler and Fritz London's 1927 quantum account of the covalent bond of the hydrogen molecule.
The application of quantum mechanics to fields rather than single particles, resulting in what are known as quantum field theories, began in 1927. 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. The renormalization procedure for eliminating the awkward infinite predictions of quantum field theory was first implemented in QED. (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.
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. and its Dirac adjoint are the fields representing electrically charged particles, specifically electron and positron fields represented as Dirac spinors. is the gauge covariant derivative, with the coupling strength (equal to the elementary charge), the covariant vector potential of the electromagnetic field and the electromagnetic field tensor.
Euler-Lagrange equations
To begin, plug in the definition of D into the Lagrangian to see that L is
One can plug this Lagrangian into the Euler-Lagrange equation of motion for a field
to find the field equations for QED.
The two terms from this lagrangian are then
Plugging these two back into the Euler-Lagrange equation (2) results in
and the complex conjugate
If you bring the middle term to the right-hand side looks like:
The left hand side is like the original Dirac equation and the left-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, Aμ:
The two terms this time are
And these two terms, when plugged back into (3) give
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.
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