A rigorous path integral for supersymmetic quantum mechanics and the heat kernel

DOI10.1007/s00220-008-0606-2zbMath1158.81016arXiv0705.0638OpenAlexW3104513366MaRDI QIDQ2517959

Stephen F. Sawin, Dana Stanley Fine

Publication date: 12 January 2009

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0705.0638

Mathematics Subject Classification ID

Path integrals in quantum mechanics (81S40) Supersymmetry and quantum mechanics (81Q60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Heat kernels in several complex variables (32W30)

Related Items (5)

A rigorous construction of the supersymmetric path integral associated to a compact spin manifold ⋮ Path integrals, supersymmetric quantum mechanics, and the Atiyah-Singer index theorem for twisted Dirac ⋮ Strong short-time asymptotics and convolution approximation of the heat kernel ⋮ Short-time asymptotics of a rigorous path integral for N = 1 supersymmetric quantum mechanics on a Riemannian manifold ⋮ The Chern character of \(\vartheta \)-summable Fredholm modules over dg algebras and localization on loop space

Cites Work

• The Mathai-Quillen formalism and topological field theory
• Superconnections, Thom classes, and equivariant differential forms
• A short proof of the local Atiyah-Singer index theorem
• Supersymmetry and Morse theory
• Curvature and the eigenforms of the Laplace operator
• Path integrals on manifolds by finite dimensional approximation
• Stochastic calculus in superspace. II. Differential forms, supermanifolds and the Atiyah-Singer index theorem
• SUPERSYMMETRY AND BROWNIAN MOTION ON SUPERMANIFOLDS
• On certain systems of parabolic equations
• Supersymmetry and the Atiyah-Singer index theorem

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