Extravariables in the BRST Quantization of Second-Class Constrained Systems; Existence Theorems

Abstract

In this paper we show how the BRST quantization can be applied to systems possessing only second-class constraints through their conversion to some first-class ones starting with our method exposed in [Nucl.Phys. B456 (1995)473]. Thus, it is proved that i) for a certain class of second-class systems there exists a standard coupling between the variables of the original phase-space and some extravariables such that we can transform the original system into a one-parameter family of first-class systems; ii) the BRST quantization of this family in a standard gauge leads to the same path integral as that of the original system. The analysis is accomplished in both reducible and irreducible cases. In the same time, there is obtained the Lagrangian action of the first-class family and its provenience is clarified. In this context, the Wess-Zumino action is also derived. The results from the theoretical part of the paper are exemplified in detail for the massive Yang-Mills theory and for the massive abelian three-form gauge fields.

LaTeX, 37 pages; Correctly formatted version; The authors may be reached at e-mail address: [email protected]

References in corpus (6)

• Batalin-Tyutin Quantisation of the $C{P}^{N-1}$ model
• A note on the path integral for systems with primary and secondary second class constraints
• Batalin-Tyutin Quantization of the Self-Dual Massive Theory in Three Dimensions
• Gauge Equivalence in Two--Dimensional Gravity
• Gauge Invariance and Second Class Constraints in 3-D Linearized Gravity
• Canonical Covariant Formulation of Green-Schwarz Superstring without Second Class Constraints

Cited by in corpus (2)

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