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Covariant Gauge Fixing and Canonical Quantization | | D. G. C. McKeon
; | | Date: |
15 Dec 2011 | | Abstract: | Theories that contain first class constraints possess gauge invariance which
results in the necessity of altering the measure in the associated quantum
mechanical path integral. If the path integral is derived from the canonical
structure of the theory, then the choice of gauge conditions used in
constructing Faddeev’s measure cannot be covariant. This shortcoming is
normally overcome either by using the "Faddeev-Popov" quantization procedure,
or by the approach of Batalin-Fradkin-Fradkina-Vilkovisky, and then
demonstrating that these approaches are equivalent to the path integral
constructed from the canonical approach with Faddeev’s measure. We propose in
this paper an alternate way of defining the measure for the path integral when
it is constructed using the canonical procedure for theories containing first
class constraints and that this new approach can be used in conjunction with
covariant gauges. This procedure follows the Faddeev-Popov approach, but rather
than working with the form of the gauge transformation in configuration space,
it employs the generator of the gauge transformation in phase space. We
demonstrate this approach to the path integral by applying it to Yang-Mills
theory, a spin-two field and the first order Einstein-Hilbert action in two
dimensions. The problems associated with defining the measure for theories
containing second-class constraints and ones in which there are fewer secondary
first class constraints than primary first class constraints are discussed. | | Source: | arXiv, 1112.3646 | | Services: | Forum | Review | PDF | Favorites | |
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