Everything about Quantum Electrodynamics totally explained
Quantum electrodynamics (
QED) is a
relativistic quantum field theory of
electrodynamics. QED was developed by a number of physicists, beginning in the late 1920s. It describes some aspects of how electrons, positrons and photons interact. 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.
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 by
André-Marie Ampère in 1822. The word 'quantum', as used in physics, for example 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 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 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 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
velocity c on average.
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. 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. The paths 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's 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 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),
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 the symmetry group
U(1) as
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
» :
