What is Quantum Electrodynamics (QED)?

Quantum Electrodynamics (QED for short) is the most mature branch of quantum field theory.

Quantum electrodynamics is

Shortly after the establishment of quantum mechanics in 1925, PAM Dirac proposed the quantum theory of radiation in 1927, WK Heisenberg, and W. Pauli in 1929, laying the theoretical foundation for quantum electrodynamics.

Within the scope of quantum mechanics, the interaction between charged particles and electromagnetic fields can be used as a perturbation to deal with the absorption and stimulated emission of light, but it cannot deal with the problem of self-emission of light. Because if the electromagnetic field is considered as a classical field, there is no radiation field at all before the photon is emitted. An excited electron in an atom is a stationary state in quantum mechanics. Without a radiation field as a perturbation, it will not undergo transitions. Self-emission is the fact of existence. In order to explain this phenomenon and to give it a quantitative probability, it can only be handled in quantum mechanics.

One method is to use the corresponding principle to treat the electrons in the excited state of the atom as the sum of many harmonic oscillators, and determine that the oscillating current that generates radiation corresponds to some transition matrix elements of quantum mechanics, to calculate the self-emitting transition probability. From this processing method, M. Planck's radiation formula can be obtained, which in turn shows that the corresponding principle processing is feasible.

Another approach is to use A. Einstein's relationship between the probability of self-emission and the probability of absorption. Although the results obtained by these methods can be consistent with the experimental results, in theory, they are in contradiction with the quantum mechanical system-the stationary life of quantum mechanics is infinite.

Quantum electrodynamic radiation field

Dirac, Heisenberg and Pauli quantify the radiation field. In addition to obtaining a clear representation of the wave-particle duality of light, the above contradictions are also resolved. After the electromagnetic field is quantized, the electric field strength

And magnetic field strength

All become operators. Each component of them satisfies a certain reciprocity relationship. Their "expected value" (ie, the average value measured in the experiment) should satisfy the uncertainty relationship of quantum mechanics. They cannot have a certain value at the same time (that is, the mean square error is zero at the same time). ). As a special case, they cannot be determined to be zero at the same time. In a state where no photons exist (it is called the vacuum state of the radiation field),

with

The average is zero. but

versus

The average value of is not zero (otherwise mean square; the difference is also zero at the same time). This is the vacuum fluctuation of the quantized radiation field. It is very similar to the zero energy of a harmonic oscillator in quantum mechanics. After the quantization of the field, the generation and annihilation become a universal and basic process. Therefore, when an atom is in an excited state, although no photon exists, the electron can still transition to a low energy state and generate a photon. Starting from the expression of quantum theory of radiation field, we can calculate the cross-sections of various basic processes of interaction between charged particles and electromagnetic field, such as Compton effect, photoelectric effect, induced radiation, electron pair generation and electron pair annihilation. These results are obtained by using the perturbation method to obtain the lowest non-zero approximation, which is in good agreement with the experiment. But no matter what kind of process, when calculating the result of the higher-level approximation, we must encounter divergence difficulties, that is, get infinite results. This was first pointed out by JR Oppenheimer in 1930. In the following ten years or so, although research on many fundamental electromagnetic processes, as well as research on the penetration of high-energy radiation in matter and cascade showers of cosmic rays, quantum electrodynamics continued to develop, but in solving basic Diffusion difficulties in theory are still relatively stagnant.

Quantum electrodynamics correction

The calculation of higher-order corrections of various processes was carried out under the new theoretical expression form. These results all meet the increasing requirements of the theory due to the improvement of experimental conditions and accuracy. Quantum electrodynamics is a theory of gauge fields. The unification of electromagnetic interaction and weak interaction is an important development stage of quantum field theory. Standard models of the unified theory of electroweakness and quantum chromodynamics describing strong interactions belong to the category of gauge field theory. Both of them are learned from the theory and methods of quantum electrodynamics. The renormalization theory established from the study of quantum electrodynamics is not only used in particle physics, but is also a useful tool for statistical physics (see Phases and Phase Transitions, Renormalization Groups). ^[1]