1,830 research outputs found

### Multiplicative anomaly and zeta factorization

Some aspects of the multiplicative anomaly of zeta determinants are
investigated. A rather simple approach is adopted and, in particular, the
question of zeta function factorization, together with its possible relation
with the multiplicative anomaly issue is discussed. We look primordially into
the zeta functions instead of the determinants themselves, as was done in
previous work. That provides a supplementary view, regarding the appearance of
the multiplicative anomaly. Finally, we briefly discuss determinants of zeta
functions that are not in the pseudodifferential operator framework.Comment: 20 pages, AIP styl

### Casimir effect in rugby-ball type flux compactifications

As a continuation of the work in \cite{mns}, we discuss the Casimir effect
for a massless bulk scalar field in a 4D toy model of a 6D warped flux
compactification model,to stabilize the volume modulus. The one-loop effective
potential for the volume modulus has a form similar to the Coleman-Weinberg
potential. The stability of the volume modulus against quantum corrections is
related to an appropriate heat kernel coefficient. However, to make any
physical predictions after volume stabilization, knowledge of the derivative of
the zeta function, $\zeta'(0)$ (in a conformally related spacetime) is also
required. By adding up the exact mass spectrum using zeta function
regularization, we present a revised analysis of the effective potential.
Finally, we discuss some physical implications, especially concerning the
degree of the hierarchy between the fundamental energy scales on the branes.
For a larger degree of warping our new results are very similar to the previous
ones \cite{mns} and imply a larger hierarchy. In the non-warped (rugby-ball)
limit the ratio tends to converge to the same value, independently of the bulk
dilaton coupling.Comment: 13 pages, 6 figures, accepted for publication in PR

### Complex fermion mass term, regularization and CP violation

It is well known that the CP violating theta term of QCD can be converted to
a phase in the quark mass term. However, a theory with a complex mass term for
quarks can be regularized so as not to violate CP, for example through a zeta
function. The contradiction is resolved through the recognition of a dependence
on the regularization or measure. The appropriate choice of regularization is
discussed and implications for the strong CP problem are pointed out.Comment: REVTeX, 4 page

### Uses of zeta regularization in QFT with boundary conditions: a cosmo-topological Casimir effect

Zeta regularization has proven to be a powerful and reliable tool for the
regularization of the vacuum energy density in ideal situations. With the
Hadamard complement, it has been shown to provide finite (and meaningful)
answers too in more involved cases, as when imposing physical boundary
conditions (BCs) in two-- and higher--dimensional surfaces (being able to
mimic, in a very convenient way, other {\it ad hoc} cut-offs, as non-zero
depths). What we have considered is the {\it additional} contribution to the cc
coming from the non-trivial topology of space or from specific boundary
conditions imposed on braneworld models (kind of cosmological Casimir effects).
Assuming someone will be able to prove (some day) that the ground value of the
cc is zero, as many had suspected until very recently, we will then be left
with this incremental value coming from the topology or BCs. We show that this
value can have the correct order of magnitude in a number of quite reasonable
models involving small and large compactified scales and/or brane BCs, and
supergravitons.Comment: 9 pages, 1 figure, Talk given at the Seventh International Workshop
Quantum Field Theory under the Influence of External Conditions, QFEXT'05,
Barcelona, September 5-9, 200

### An Extension of the Chowla-Selberg Formula Useful in Quantizing with the Wheeler-De Witt Equation

The two-dimensional inhomogeneous zeta-function series (with homogeneous part
of the most general Epstein type): \sum_{m,n \in \mbox{\bf Z}}
(am^2+bmn+cn^2+q)^{-s}, is analytically continued in the variable $s$ by
using zeta-function techniques. A simple formula is obtained, which extends the
Chowla-Selberg formula to inhomogeneous Epstein zeta-functions. The new
expression is then applied to solve the problem of computing the determinant of
the basic differential operator that appears in an attempt at quantizing
gravity by using the Wheeler-De Witt equation in 2+1 dimensional spacetime with
the torus topology.Comment: 14 pages (small typo errors corrected and 2page improvement of
physical applications), LaTeX file, UB-ECM-PF 94/

### On two complementary approaches aiming at the definition of the determinant of an elliptic partial differential operator

We bring together two apparently disconnected lines of research (of
mathematical and of physical nature, respectively) which aim at the definition,
through the corresponding zeta function, of the determinant of a differential
operator possessing, in general, a complex spectrum. It is shown explicitly how
the two lines have in fact converged to a meeting point at which the precise
mathematical conditions for the definition of the zeta function and the
associated determinant are easy to understand from the considerations coming up
from the physical approach, which proceeds by stepwise generalization starting
from the most simple cases of physical interest. An explicit formula that
establishes the bridge between the two approaches is obtained.Comment: LaTeX file, 9 pages, no figure

### A comment on the theory of turbulence without pressure proposed by Polyakov

Owing to its lack of derivability, the dissipative anomaly operator appearing
in the theory of turbulence without pressure recently proposed by Polyakov
appears to be quite elusive. In particular, we give arguments that seem to lead
to the conclusion that an anomaly in the first equation of the sequence of
conservation laws cannot be {\it a priori} excluded.Comment: Argument enforced, references added, LaTeX file, 6 pages, no figure

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