On Quantum Integrability and the Lefschetz Number

Details On Quantum Integrability and the Lefschetz Number On Quantum Integrability and the Lefschetz Number

1993-05-18

arxiv.org/abs/hep-th/9305077v1

Mod.Phys.Lett.A8:2311-2322,1993

Physics

High Energy Physics

High Energy Physics - Theory

11 pages

Scientific paper

10.1142/S0217732393003615

Certain phase space path integrals can be evaluated exactly using equivariant cohomology and localization in the canonical loop space. Here we extend this to a general class of models. We consider hamiltonians which are {\it a priori} arbitrary functions of the Cartan subalgebra generators of a Lie group which is defined on the phase space. We evaluate the corresponding path integral and find that it is closely related to the infinitesimal Lefschetz number of a Dirac operator on the phase space. Our results indicate that equivariant characteristic classes could provide a natural geometric framework for understanding quantum integrability.

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