Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Physical Properties of Quantum Field Theory Measures   Well known methods of measure theory on infinite dimensional spaces are used
to study physical properties of measures relevant to quantum field theory. The
difference of typical configurations of free massive scalar field theories with
different masses is studied. We apply the same methods to study the
Ashtekar-Lewandowski (AL) measure on spaces of connections. We prove that the
diffeomorphism group acts ergodically, with respect to the AL measure, on the
Ashtekar-Isham space of quantum connections modulo gauge transformations. We
also prove that a typical, with respect to the AL measure, quantum connection
restricted to a (piecewise analytic) curve leads to a parallel transport
discontinuous at every point of the curve.

10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ