Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Index-free Heat Kernel Coefficients   Using index-free notation, we present the diagonal values of the first five
heat kernel coefficients associated with a general Laplace-type operator on a
compact Riemannian space without boundary. The fifth coefficient appears here
for the first time. For a flat space with a gauge connection, the sixth
coefficient is given too. Also provided are the leading terms for any
coefficient, both in ascending and descending powers of the Yang-Mills and
Riemann curvatures, to the same order as required for the fourth coefficient.
These results are obtained by directly solving the relevant recursion
relations, working in Fock-Schwinger gauge and Riemann normal coordinates. Our
procedure is thus noncovariant, but we show that for any coefficient the
`gauged' respectively `curved' version is found from the corresponding
`non-gauged' respectively `flat' coefficient by making some simple covariant
substitutions. These substitutions being understood, the coefficients retain
their `flat' form and size. In this sense the fifth and sixth coefficient have
only 26 and 75 terms respectively, allowing us to write them down. Using
index-free notation also clarifies the general structure of the heat kernel
coefficients. In particular, in flat space we find that from the fifth
coefficient onward, certain scalars are absent. This may be relevant for the
anomalies of quantum field theories in ten or more dimensions.

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The categories of this paper are: math
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph