FIZIKA B 18 (2009) 3, 99-140

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DIRAC FUNDAMENTAL QUANTIZATION OF GAUGE THEORIES IS THE NATURAL WAY OF REFERENCE FRAMES IN MODERN PHYSICS

L. D. LANTSMAN
Wissenschaftliche Gesellschaft bei Jüdische Gemeinde zu Rostock,
Augusten Strasse, 20, 18055, Rostock, Germany
E-mail address: llantsman@freenet.de

Received 3 September 2007;    Accepted 17 September 2008
Online 13 July 2009

We analyse two known principal approaches to the quantization of physical models. They are the Faddeev-Popov (FP) "heuristic" approach, based on fixing a gauge in the FP path integrals formalism, and the "fundamental" approach of Dirac based on the constraint-shell reduction of Hamiltonians with deleting of unphysical variables. The relativistically invariant FP "heuristic" approach deals with a small class of problems associated with S-matrices squared considering on-shell quantum fields. On the other hand, the "fundamental" quantization approach of Dirac involves the manifest relativistic covariance of quantum fields that survive the constraint-shell reduction of Hamiltonians. One can apply this approach to a broader class of problems than by studying S-matrices. Investigations of various bound states in QED and QCD are examples of such applications. In the present study, with the example of the Dirac "fundamental" quantization of the Minkowskian non-Abelian Higgs model (studied in its historical retrospective), we show obvious advantages of this quantization approach. The arguments in favour of the Dirac fundamental quantization of a physical model will be presented as a way of Einstein and Galilei relativity in modern physics.

PACS numbers: 11.10.Ef, 14.80.Bn, 14.80.Hv
UDC 530.145, 539.12

Keywords: non-Abelian theory, BPS monopole, Minkowsli space, quantization scheme

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