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- W1963977679 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." @default.
- W1963977679 created "2016-06-24" @default.
- W1963977679 creator A5033301606 @default.
- W1963977679 date "2012-03-01" @default.
- W1963977679 modified "2023-09-27" @default.
- W1963977679 title "Covariant gauge fixing and canonical quantization" @default.
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- W1963977679 doi "https://doi.org/10.1139/p2012-013" @default.
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