Dirac equation quantum light theory

The Dirac equation describes the quantum-mechanical motion of particles with spin-1/2 according to the requirements of the special theory of relativity. Correspondingly, it contains the following scalar parameters Planck s constant h, which sets the scale of quantum phenomena, the velocity of light c, which sets the scale for relativistic effects, and m, the rest-mass of the particle. 

However, already in 1930s deviations were observed between the results of precision spectroscopy and the Dirac theory for simple atomic systems, primarily for the hydrogen atom. The existence of negative-energy states in the solutions of Dirac equation is the mathematical but not the physical grounds of the existence of particles and antiparticles (electrons and positrons). Besides, the velocity of light is finite. For an complete model we must turn to quantum field theory and quantum electrodynamics (QED) [4]. 

The Schrodinger equation, however, does not take into account relativity, which is important when particles move at about the speed of light. So, P.A.M. Dirac (1928) advanced his theory of relativistic quantum theory, introducing time as the fourth dimension. 

Dirac s 1929 comment [227] The underlying physical laws necessary for the mathematical theory for a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too difficult to be soluble has become a part of the Delphic wisdom of our subject. To this confident statement Richard Feynman [228] added in 1985 a codicil But there was still the problem of the interaction of light and matter , and . .. the theory behind chemistry is quantum electrodynamics . He goes on to say that he is writing of non-covariant quantum electrodynamics, for the interaction of the radiation field with the slow-moving particles in atoms and molecules. 

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