Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-perturbative Quantum Propagators in Bounded Spaces   We outline a new approach to calculating the quantum mechanical propagator in
the presence of geometrically non-trivial Dirichlet boundary conditions based
upon a generalisation of an integral transform of the propagator studied in
previous work (the so-called ``hit function''), and a convergent sequence of
Pad\'e approximants. In this paper the generalised hit function is defined as a
many-point propagator and we describe its relation to the sum over trajectories
in the Feynman path integral. We then show how it can be used to calculate the
Feynman propagator. We calculate analytically all such hit functions in $D=1$
and $D=3$ dimensions, giving recursion relations between them in the same or
different dimensions and apply the results to the simple cases of propagation
in the presence of perfectly conducting planar and spherical plates. We use
these results to conjecture a general analytical formula for the propagator
when Dirichlet boundary conditions are present in a given geometry, also
explaining how it can be extended for application for more general,
non-localised potentials. Our work has resonance with previous results obtained
by Grosche in the study of path integrals in the presence of delta potentials.
We indicate the eventual application in a relativistic context to determining
Casimir energies using this technique.

34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an