Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heat Kernel Asymptotics of the Gilkey-Smith Boundary Value Problem   The formulation of gauge theories on compact Riemannian manifolds with
boundary leads to partial differential operators with Gilkey--Smith boundary
conditions, whose peculiar property is the occurrence of both normal and
tangential derivatives on the boundary. Unlike the standard Dirichlet or
Neumann boundary conditions, this boundary-value problem is not automatically
elliptic but becomes elliptic under certain conditions on the boundary
operator. We study the Gilkey--Smith boundary-value problem for Laplace-type
operators and find a simple criterion of ellipticity. The first non-trivial
coefficient of the asymptotic expansion of the trace of the heat kernel is
computed and the local leading asymptotics of the heat-kernel diagonal is also
obtained. It is shown that, in the non-elliptic case, the heat-kernel diagonal
is non-integrable near the boundary, which reflects the fact that the heat
kernel is not of trace class. We apply this analysis to general linear bosonic
gauge theories and find an explicit condition of ellipticity.

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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex