2,058 research outputs found
Spin on the 4-ball
Using known mode properties, the functional determinant for massless
spin-half fields on the Euclidean 4-ball is calculated and shown to be
different for spectral (nonlocal) and mixed (local) boundary conditions. The
local result agrees with that from a conformal argument. Some higher-spin
results are also given.Comment: 8p,JyTe
p-forms on d-spherical tessellations
The spectral properties of p-forms on the fundamental domains of regular
tesselations of the d-dimensional sphere are discussed. The degeneracies for
all ranks, p, are organised into a double Poincare series which is explicitly
determined. In the particular case of coexact forms of rank (d-1)/2, for odd d,
it is shown that the heat--kernel expansion terminates with the constant term,
which equals (-1)^{p+1}/2 and that the boundary terms also vanish, all as
expected. As an example of the double domain construction, it is shown that the
degeneracies on the sphere are given by adding the absolute and relative
degeneracies on the hemisphere, again as anticipated. The eta invariant on a
fundamental domain is computed to be irrational. The spectral counting function
is calculated and the accumulated degeneracy give exactly. A generalised
Weyl-Polya conjecture for p-forms is suggested and verified.Comment: 23 pages. Section on the counting function adde
Effective actions with fixed points, (error in derivation of coefficient corrected)
The specific form of the constant term in the asymptotic expansion of the
heat-kernel on an axially-symmetric space with a codimension two fixed-point
set of conical singularities is used to determine the associated conformal
change of the effective action in four dimensions. Another derivation of the
relevant coefficient is presented.Comment: 10p,uses JyTeX,MUTP/94/1
Heat kernels on curved cones
A functorial derivation is presented of a heat-kernel expansion coefficient
on a manifold with a singular fixed point set of codimension two. The existence
of an extrinsic curvature term is pointed out.Comment: 4p.,sign errors corrected and a small addition,uses JyTeX,MUTP/94/0
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