2012/07/11 by Dana S. Fine, Dana Fine, Fine, Dana +2
Mathematics · Physics and Astronomy · #53Z05 #58J20 #81Q35 #81Q60 #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #advanced mathematical theories #hep-th #math-ph #math.DG #math.MP #msc:53Z05 #msc:58J20 #msc:81Q35 #msc:81Q60
paper · pdf · doi:10.48550/arxiv.1207.2751
Minor changes in introduction, exposition and title based on referees' comments
openalex publication_date 2012/07/11 · arxiv created 2013/03/28 · arxiv updated 2013/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Following Feynman's prescription for constructing a path integral representation of the propagator of a quantum theory, a short-time approximation to the propagator for imaginary time, N=1 supersymmetric quantum mechanics on a compact, even-dimensional Riemannian manifold is constructed. The path integral is interpreted as the limit of products, determined by a partition of a finite time interval, of this approximate propagator. The limit under refinements of the partition is shown to converge uniformly to the heat kernel for the Laplace-Beltrami operator on forms. A version of the steepest descent approximation to the path integral is obtained, and shown to give the expected short-time behavior of the supertrace of the heat kernel.