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arXiv · hep-th/9305077

On Quantum Integrability and the Lefschetz Number

A. J. Niemi·K. Palo
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Abstract

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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A. J. Niemi, K. Palo. 1993-05-18. On Quantum Integrability and the Lefschetz Number. https://doi.org/10.1142/s0217732393003615

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