Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gauge theories on manifolds with boundary   The boundary-value problem for Laplace-type operators acting on smooth
sections of a vector bundle over a compact Riemannian manifold with generalized
local boundary conditions including both normal and tangential derivatives is
studied. The condition of strong ellipticity of this boundary-value problem is
formulated. The resolvent kernel and the heat kernel in the leading
approximation are explicitly constructed. As a result, the previous work in the
literature on heat-kernel asymptotics is shown to be a particular case of a
more general structure. For a bosonic gauge theory on a compact Riemannian
manifold with smooth boundary, the problem is studied of obtaining a
gauge-field operator of Laplace type, jointly with local and gauge-invariant
boundary conditions, which should lead to a strongly elliptic boundary-value
problem. The scheme is extended to fermionic gauge theories by means of local
and gauge-invariant projectors. After deriving a general condition for the
validity of strong ellipticity for gauge theories, it is proved that for
Euclidean Yang--Mills theory and Rarita--Schwinger fields all the above
conditions can be satisfied. For Euclidean quantum gravity, however, this
property no longer holds, i.e. the corresponding boundary-value problem is not
strongly elliptic. Some non-standard local formulae for the leading asymptotics
of the heat-kernel diagonal are also obtained. It is shown that, due to the
absence of strong ellipticity, the heat-kernel diagonal is non-integrable near
the boundary.

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The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg