3.5.3 Quantum Electrodynamics
The basic idea behind Quantum Field Theory is that the electromagnetic field should be represented by matrices in the same way that position and momentum were represented in Quantum Mechanics. The ideas of Quantum Mechanics were thus extended to systems having an infinite number of degrees of freedom, as infinite array of quantum oscillators. This was started in 1927, by Dirac, in his famous paper on “the quantum theory of the emission and absorption of radiation”, in which he coined the name “Quantum Electrodynamics” (QED), which was the first Quantum Field Theory (QFT).
In his paper, Dirac proposed a systematic procedure for transferring the characteristic quantum phenomenon, or the discreteness of physical quantities, from the quantum-mechanical treatment of particles to fields. Employing the theory of the quantum harmonic oscillator, Dirac gave a theoretical description of how photons appear in the quantization of the electromagnetic field. Later, Dirac’s procedure became a model for the quantization of other fields, as will be described further in section 5. Quantum Electrodynamics is, therefore, based on the quantization of the electromagnetic field, in addition to the relativistic theory of the electron from the Dirac wave equation that we discussed in section 5.2.
In QED, electric charges are the sources of the electric field, which exerts a force on any particles that carry electric charges, such as electrons, protons, and quarks. As a result, these electric charges move, and a current flows, and a magnetic field is then produced. The changing magnetic field, in turn, causes electric current. The physical description of these interacting charged particles, electrical currents, electrical fields, and magnetic fields is called Electromagnetism, and QED is a relativistic quantum theory of Electromagnetism.
This first approach by Dirac was developed further with contributions from Pauli, Heisenberg, Fermi and Wigner. In the beginning, physicists believed that with QED it is possible to perform any computation for any physical process involving photons and charged particles. However, further studies in 1937 and 1939, revealed that such computations were reliable only at a first order of perturbation theory. At higher orders in the series infinities emerged, making such computations meaningless and casting serious doubts on the internal consistency of the theory itself.
More difficulties with QED theory were realized in the 1940s, due to further discrepancies after the improvements in microwave technology made it possible to take more precise measurements of the shift of the levels of a hydrogen atom, now known as the Lamb shift and magnetic moment of the electron.
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