Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetrized Trace and Symmetrized Determinant of Odd Class
  Pseudo-Differential Operators   We introduce a new canonical trace on odd class logarithmic
pseudo-differential operators on an odd dimensional manifold, which vanishes on
commutators. When restricted to the algebra of odd class classical
pseudo-differential operators our trace coincides with the canonical trace of
Kontsevich and Vishik. Using the new trace we construct a new determinant of
odd class classical elliptic pseudo-differential operators. This determinant is
multiplicative up to sign whenever the multiplicative anomaly formula for usual
determinants of Kontsevich-Vishik and Okikiolu holds. When restricted to
operators of Dirac type our determinant provides a sign refined version of the
determinant constructed by Kontsevich and Vishik. We discuss some applications
of the symmetrized determinant to a non-linear $\sigma$-model in
superconductivity.

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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org