Velocity quantum electrodynamics

Rate of change of observables, 477 Ray in Hilbert space, 427 Rayleigh quotient, 69 Reduction from functional to algebraic form, 97 Regula fold method, 80 Reifien, B., 212 Relative motion of particles, 4 Relative velocity coordinate system and gas coordinate system, 10 Relativistic invariance of quantum electrodynamics, 669 Relativistic particle relation between energy and momentum, 496 Relativistic quantum mechanics, 484 Relaxation interval, 385 method of, 62 oscillations, 383 asymptotic theory, 388 discontinuous theory, 385 Reliability, 284... 

In previous chapters we considered elementary crystal excitation taking into account only the Coulomb interaction between carriers. From the point of view of quantum electrodynamics (see, for example, (1)) such an interaction is conditioned by an exchange of virtual scalar and longitudinal photons, so that the potential energy, corresponding to this interaction, depends on the carrier positions and not on their velocity distribution. As is well-known, the exchange of virtual transverse photons leads to the so-called retarded interaction between charges. 

In this chapter, we shall reassess some of the physical implications of the Dirac equation [5, 6], which were somehow overlooked in the sophisticated formal developments of quantum electrodynamics. We will conjecture that the internal structure of the electron should consist of a massless charge describing at light velocity an oscillatory motion (Zitterbewegung) in a small domain defined by the Compton wavelength, the observed spin momentum and rest mass being jointly generated by this very internal motion. 

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]. 

To explain these differences the quantum electrodynamic corrections have to be implemented. The velocity of light is finite and this means retardation of the interparticle interactions. This means that the Dirac-Coulomb Hamiltonian has to be corrected by further expressions. 

CPD=Chang - Pelissier- Durand DCB = Dirac - Coulomb -Breit DHF = Dirac-Hartree-Fock DK = Douglas-Kroll FORA = first-order regular approximation MVD = mass-velocity-Darwin term QED = quantum electrodynamics ZORA = zero-order regular approximation. 

In the last chapter the basic framework of classical nonrelativistic mechanics has been developed. This theory crucially relies on the Galilean principle of relativity (cf. section 2.1.2), which does not match experimental results for high velocities and therefore has to be replaced by the more general relativity principle of Einstein. It will directly lead to classical relativistic mechanics and electrodynamics, where again the term classical is used to distinguish this theory from the corresponding relativistic quantum theory to be presented in later chapters. 

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