1,027 research outputs found
Spherical Casimir energies and Dedekind sums
Casimir energies on space-times having general lens spaces as their spatial
sections are shown to be given in terms of generalised Dedekind sums related to
Zagier's. These are evaluated explicitly in certain cases as functions of the
order of the lens space. An easily implemented recursion approach is used.Comment: 18 pages, 2 figures, v2:typos corrected, inessential equation in
Discussion altered. v3:typos corrected, 1 reference and comments added.
v4:typos corrected. Ancillary results added in an appendi
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
Zero modes, entropy bounds and partition functions
Some recent finite temperature calculations arising in the investigation of
the Verlinde-Cardy relation are re-analysed. Some remarks are also made about
temperature inversion symmetry.Comment: 12 pages, JyTe
Wormhole Effects on Yang-Mills Theory
In this paper wormhole effects on YM theory are examined. The
wormhole wave functions for the scalar, the vector and the tensor expansion
modes are computed assuming a small gauge coupling which leads to an effective
decoupling of gravity and YM theory. These results are used to determine the
wormhole vertices and the corresponding effective operators for the lowest
expansion mode of each type. For the lowest scalar mode we find a
renormalization of the gauge coupling from the two point function and the
operators \tr (F^3), \tr (F^2\tilde{F}) from the three point function. The
two point function for the lowest vector mode contributes to the gauge coupling
renormalization only whereas the lowest tensor mode can also generate higher
derivative terms.Comment: 15 pages, TUM--TH--165/9
The Dirac-Dowker Oscillator
The oscillator-like interaction is introduced in the equation for the
particle of arbitrary spin, given by Dirac and re-written to a matrix form by
Dowker.Comment: LaTeX file, 4pp. Preprint EFUAZ 94-0
The C_2 heat-kernel coefficient in the presence of boundary discontinuities
We consider the heat-kernel on a manifold whose boundary is piecewise smooth.
The set of independent geometrical quantities required to construct an
expression for the contribution of the boundary discontinuities to the C_{2}
heat-kernel coefficient is derived in the case of a scalar field with Dirichlet
and Robin boundary conditions. The coefficient is then determined using
conformal symmetry and evaluation on some specific manifolds. For the Robin
case a perturbation technique is also developed and employed. The contributions
to the smeared heat-kernel coefficient and cocycle function are calculated.
Some incomplete results for spinor fields with mixed conditions are also
presented.Comment: 25 pages, LaTe
Determinants on lens spaces and cyclotomic units
The Laplacian functional determinants for conformal scalars and coexact
one-forms are evaluated in closed form on inhomogeneous lens spaces of certain
orders, including all odd primes when the essential part of the expression is
given, formally as a cyclotomic unitComment: 18 pages, 1 figur
Heat-kernels and functional determinants on the generalized cone
We consider zeta functions and heat-kernel expansions on the bounded,
generalized cone in arbitrary dimensions using an improved calculational
technique. The specific case of a global monopole is analysed in detail and
some restrictions thereby placed on the coefficient. The computation
of functional determinants is also addressed. General formulas are given and
known results are incidentally, and rapidly, reproduced.Comment: 26p,LaTeX.(Cosmetic changes and eqns (9.8),(11.2) corrected.
K-causality and degenerate spacetimes
The causal relation was introduced by Sorkin and Woolgar to extend the
standard causal analysis of spacetimes to those that are only . Most
of their results also hold true in the case of spacetimes with degeneracies. In
this paper we seek to examine explicitly in the case of Lorentzian
topology changing Morse spacetimes containing isolated degeneracies. We first
demonstrate some interesting features of this relation in globally Lorentzian
spacetimes. In particular, we show that is robust and that it coincides
with the Seifert relation when the spacetime is stably causal. Moreover, the
Hawking and Sachs characterisation of causal continuity translates into a
natural expression in terms of for general spacetimes. We then examine
in topology changing Morse spacetimes both with and without the
degeneracies and find further characterisations of causal continuity.Comment: Latex, 23 pages, 4 figure
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