On the Gupta-Bleuler and Dirac-Fock Quantization Schemes Revisited
Abstract
The classical Gupta-Bleuler quantization scheme in quantum electromagnetic field theory, based on the so-called “weakened” Lorenz subsidiary condition and indefinite metric on the reduced Fock space, is revisited within the canonical Dirac-Fock quantization approach. The latter, as applied to the Fermi-Fock-Podolsky Lagrangian, allowed both to satisfy the strong Lorenz subsidiary condition on the Fock space and to prove its averaged invariance in time, as well as to state positive energy density definiteness of quantum photon states. There is also demonstrated both the time-noninvariance of the averaged "weakened" Lorenz subsidiary condition within the Gupta and Bleuler approach and the resulting energy density positive nondefiniteness. We also reanalized the corresponding N.N. Bogolubov’s (Sr.) variational approach to constructing a deformed strong Lorenz type operator condition both within the perturbative Scwinger’s S-matrix approach and within the Fock many-temporal paradigm. A short supplement is devoted to analysis of the classical Lorenz-type subsidiary condition and the related temporal invariance of the electric potential energy, providing a derivation of the complete system of classical Maxwell’s equations.
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