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Reduction of quantum systems with arbitrary first class constraints and Hecke algebras

A. Sevostyanov
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Abstract

We propose a method for reduction of quantum systems with arbitrary first class constraints. An appropriate mathematical setting for the problem is homology of associative algebras. For every such an algebra $A$ and its subalgebra B with an augmentation e there exists a cohomological complex which is a generalization of the BRST one. Its cohomology is an associative graded algebra Hk^{*}(A,B) which we call the Hecke algebra of the triple (A,B,e). It acts in the cohomology space H^{*}(B,V) for every left A- module V. In particular the zeroth graded component Hk^{0}(A,B) acts in the space of B- invariants of V and provides the reduction of the quantum system.

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BibTeXRIS

A. Sevostyanov. 1998-05-29. Reduction of quantum systems with arbitrary first class constraints and Hecke algebras. https://doi.org/10.1007/s002200050641

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