Dirac fundamental quantization of gauge theories is natural way of reference frames in modern physics

Abstract

We analyse two principal approaches to the quantization of physical models worked out to date. There are the Faddeev-Popov "heuristic" approach, based on fixing a gauge in the FP path integrals formalism, and the "fundamental" approach by Dirac based on the constraint-shell reduction of Hamiltonians with deleting unphysical variables. The relativistic invariant FP "heuristic" approach deals with the enough small class of problems associated with S-matrices squared taking on-shell of quantum fields. On the other hand, the "fundamental" quantization approach by Dirac involves the manifest relativistic covariance of quantum fields survived the constraint-shell reduction of Hamiltonians. This allows to apply this approach for the more broad class of problems than studying S-matrices. Researches about various bound states in QED and QCD are patterns of such applications. In the present study, with the example of the Dirac "fundamental" quantization of the Minkowskian non-Abelian Higgs model (us studied in its historical retrospective), we make sure in obvious advantages of this quantization approach. The arguments in favour of the Dirac fundamental quantization of physical model as a way of Einstein and Galilei relativity in modern physic will be presented.

v5; the specific approach to the mass gab problem in the Minkowskian BPS monopole model quantized by Dirac was pointed (see p.37 of the present issue); some references are added

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• Whether the vacuum manifold in the Minkowskian non-Abelian model quantized by Dirac can be described with the aid of the superselection rules?
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