Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Yang-Mills measure on compact surfaces   We construct and study the Yang-Mills measure in two dimensions. According to
the informal description given by the physicists, it is a probability measure
on the space of connections modulo gauge transformations on a principal bundle
with compact structure group. We are interested in the case where the base
space of this bundle is a compact orientable surface.
  The construction of the measure in a discrete setting, where the base space
of the fiber bundle is replaced by a graph traced on a surface, is quite well
understood thanks to the work of E. Witten. In contrast, the continuum limit of
this construction, which should allow to put a genuine manifold as base space,
still remains problematic.
  This work presents a complete and unified approach of the discrete theory and
of its continuum limit. We give a geometrically consistent definition of the
Yang-Mills measure, under the form of a random holonomy along a wide, intrinsic
and natural class of loops. This definition allows us to study combinatorial
properties of the measure, like its Markovian behaviour under the surgery of
surfaces, as well as properties specific to the continuous setting, for
example, some of its microscopic properties. In particular, we clarify the
links between the Yang-Mills measure and the white noise and show that there is
a major difference between the Abelian and semi-simple theories. We prove that
it is possible to construct a white noise using the measure as a starting point
and vice versa in the Abelian case but we show a result of asymptotic
independence in the semi-simple case which suggests that it is impossible to
extract a white noise from the measure.

32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess