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

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

1998-05-28

arxiv.org/abs/math/9805134v2

Mathematics

Quantum Algebra

15 pages, LaTeX 2e

Scientific paper

10.1007/s002200050641

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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