144 research outputs found
The trace of the heat kernel on a compact hyperbolic 3-orbifold
The heat coefficients related to the Laplace-Beltrami operator defined on the
hyperbolic compact manifold H^3/\Ga are evaluated in the case in which the
discrete group \Ga contains elliptic and hyperbolic elements. It is shown
that while hyperbolic elements give only exponentially vanishing corrections to
the trace of the heat kernel, elliptic elements modify all coefficients of the
asymptotic expansion, but the Weyl term, which remains unchanged. Some physical
consequences are briefly discussed in the examples.Comment: 11 page
Exact and semiclassical approach to a class of singular integral operators arising in fluid mechanics and quantum field theory
A class of singular integral operators, encompassing two physically relevant
cases arising in perturbative QCD and in classical fluid dynamics, is presented
and analyzed. It is shown that three special values of the parameters allow for
an exact eigenfunction expansion; these can be associated to Riemannian
symmetric spaces of rank one with positive, negative or vanishing curvature.
For all other cases an accurate semiclassical approximation is derived, based
on the identification of the operators with a peculiar Schroedinger-like
operator.Comment: 12 pages, 1 figure, amslatex, bibtex (added missing label eq.11
Wigner transform and pseudodifferential operators on symmetric spaces of non-compact type
We obtain a general expression for a Wigner transform (Wigner function) on
symmetric spaces of non-compact type and study the Weyl calculus of
pseudodifferential operators on them
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