Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renormalized Integrals and a Path Integral Formula for the Heat Kernel
  on a Manifold   We introduce renormalized integrals which generalize conventional measure
theoretic integrals. One approximates the integration domain by measure spaces
and defines the integral as the limit of integrals over the approximating
spaces. This concept is implicitly present in many mathematical contexts such
as Cauchy's principal value, the determinant of operators on a Hilbert space
and the Fourier transform of an $L^p$-function.
  We use renormalized integrals to define a path integral on manifolds by
approximation via geodesic polygons. The main part of the paper is dedicated to
the proof of a path integral formula for the heat kernel of any self-adjoint
generalized Laplace operator acting on sections of a vector bundle over a
compact Riemannian manifold.

24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org