Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time-slicing approximation of Feynman path integrals on compact
  manifolds   We construct fundamental solutions to the time-dependent Schr\"odinger
equations on compact manifolds by the time-slicing approximation of the Feynman
path integral. We show that the iteration of short-time approximate solutions
converges to the fundamental solutions to the Schr\"odinger equations modified
by the scalar curvature in the uniform operator topology from the Sobolev space
to the space of square integrable functions. In order to construct the
time-slicing approximation by our method, we only need to consider broken paths
consisting of sufficiently short classical paths. We prove the convergence to
fundamental solutions by proving two important properties of the short-time
approximate solution, the stability and the consistency.

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The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat