A Rigorous Path Integral for Supersymmetric Quantum Mechanics and the Heat Kernel

Abstract

In a rigorous construction of the path integral for supersymmetric quantum mechanics on a Riemann manifold, based on Bär and Pfäffle's use of piecewise geodesic paths, the kernel of the time evolution operator is the heat kernel for the Laplacian on forms. The path integral is approximated by the integral of a form on the space of piecewise geodesic paths which is the pullback by a natural section of Mathai and Quillen's Thom form of a bundle over this space. In the case of closed paths, the bundle is the tangent space to the space of geodesic paths, and the integral of this form passes in the limit to the supertrace of the heat kernel.

14 pages, LaTeX, no figs

References in corpus (1)

• The Mathai-Quillen Formalism and Topological Field Theory

Cited by in corpus (4)

• Strong Short Time Asymptotics and Convolution Approximation of the Heat Kernel
• Path integrals, SUSY QM and the Atiyah-Singer index theorem for twisted Dirac
• The Fermionic integral on loop space and the Pfaffian line bundle
• Rigorous path integrals for supersymmetric quantum mechanics: completing the path integral proof of the index theorem