Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generating functions for local symplectic groupoids and non-perturbative
  semiclassical quantization   This paper contains three results about generating functions for
Lie-theoretic integration of Poisson brackets and their relation to
quantization. In the first, we show how to construct a generating function
associated to the germ of any local symplectic groupoid and we provide an
explicit (smooth, non-formal) universal formula $S_\pi$ for integrating any
Poisson structure $\pi$ on a coordinate space. The second result involves the
relation to semiclassical quantization. We show that the formal Taylor
expansion of $S_{t\pi}$ around $t=0$ yields an extract of Kontsevich's star
product formula based on tree-graphs, recovering the formal family introduced
by Cattaneo, Dherin and Felder in [6]. The third result involves the relation
to semiclassical aspects of the Poisson Sigma model. We show that $S_\pi$ can
be obtained by non-perturbative functional methods, evaluating a certain
functional on families of solutions of a PDE on a disk, for which we show
existence and classification.

31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol