|
FIZIKA B 18 (2009) 3, 99-140
 
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
|
