Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lagrangian fields, Calabi functions, and local symplectic groupoids   A Lagrangian field on a symplectic manifold $M$ is a family
$\Lambda=\{\Lambda_x|x \in M\}$ of pointed Lagrangian submanifolds of $M$. This
notion is a generalization of a real Lagrangian polarization for which each
$\Lambda_x$ is the leaf containing $x$. Two Lagrangian fields $\Lambda$ and
$\tilde \Lambda$ are called transversal if $\Lambda_x$ intersects
$\tilde\Lambda_x$ transversally at $x$ for every $x$. Two transversal
Lagrangian fields determine an almost para-K\"ahler structure on $M$. We
construct a local symplectic groupoid on a neighborhood of the zero section of
$T^\ast M$ from two transversal Lagrangian fields on $M$. The Lagrangian
manifold of $n$-cycles of this groupoid in $(T^\ast M)^n$ has a generating
function whose germ around the diagonal of $M^n$ is given by the $n$-point
cyclic Calabi function of a closed (1,1)-form on a neighborhood of the diagonal
of $M^2$ obtained from the symplectic form on $M$.

22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat