Theories that contain first class constraints possess gauge invariance whichresults in the necessity of altering the measure in the associated quantummechanical path integral. If the path integral is derived from the canonicalstructure of the theory, then the choice of gauge conditions used inconstructing Faddeev's measure cannot be covariant. This shortcoming isnormally overcome either by using the "Faddeev-Popov" quantization procedure,or by the approach of Batalin-Fradkin-Fradkina-Vilkovisky, and thendemonstrating that these approaches are equivalent to the path integralconstructed from the canonical approach with Faddeev's measure. We propose inthis paper an alternate way of defining the measure for the path integral whenit is constructed using the canonical procedure for theories containing firstclass constraints and that this new approach can be used in conjunction withcovariant gauges. This procedure follows the Faddeev-Popov approach, but ratherthan working with the form of the gauge transformation in configuration space,it employs the generator of the gauge transformation in phase space. Wedemonstrate this approach to the path integral by applying it to Yang-Millstheory, a spin-two field and the first order Einstein-Hilbert action in twodimensions. The problems associated with defining the measure for theoriescontaining second-class constraints and ones in which there are fewer secondaryfirst class constraints than primary first class constraints are discussed.
展开▼
