19 research outputs found
Quantum States, Thermodynamic Limits and Entropy in M-Theory
We discuss the matching of the BPS part of the spectrum for (super)membrane,
which gives the possibility of getting membrane's results via string
calculations. In the small coupling limit of M--theory the entropy of the
system coincides with the standard entropy of type IIB string theory (including
the logarithmic correction term). The thermodynamic behavior at large coupling
constant is computed by considering M--theory on a manifold with topology
. We argue that the finite temperature
partition functions (brane Laurent series for ) associated with BPS
brane spectrum can be analytically continued to well--defined functionals.
It means that a finite temperature can be introduced in brane theory, which
behaves like finite temperature field theory. In the limit (point
particle limit) it gives rise to the standard behavior of thermodynamic
quantities.Comment: 7 pages, no figures, Revtex style. To be published in the Physical
Review
Wightman function and scalar Casimir densities for a wedge with two cylindrical boundaries
Wightman function, the vacuum expectation values of the field square and the
energy-momentum tensor are investigated for a massive scalar field with general
curvature coupling parameter inside a wedge with two coaxial cylindrical
boundaries. It is assumed that the field obeys Dirichlet boundary condition on
bounding surfaces. The application of a variant of the generalized Abel-Plana
formula enables to extract from the expectation values the contribution
corresponding to the geometry of a wedge with a single shell and to present the
interference part in terms of exponentially convergent integrals. The local
properties of the vacuum are investigated in various asymptotic regions of the
parameters. The vacuum forces acting on the boundaries are presented as the sum
of self-action and interaction terms. It is shown that the interaction forces
between the separate parts of the boundary are always attractive. The
generalization to the case of a scalar field with Neumann boundary condition is
discussed.Comment: 19 pages, 3 figure
Partition Functions for the Rigid String and Membrane at Any Temperature
Exact expressions for the partition functions of the rigid string and
membrane at any temperature are obtained in terms of hypergeometric functions.
By using zeta function regularization methods, the results are analytically
continued and written as asymptotic sums of Riemann-Hurwitz zeta functions,
which provide very good numerical approximations with just a few first terms.
This allows to obtain systematic corrections to the results of Polchinski et
al., corresponding to the limits and of
the rigid string, and to analyze the intermediate range of temperatures. In
particular, a way to obtain the Hagedorn temperature for the rigid membrane is
thus found.Comment: 20 pages, LaTeX file, UB-ECM-PF 93/
Zeta function method and repulsive Casimir forces for an unusual pair of plates at finite temperature
We apply the generalized zeta function method to compute the Casimir energy
and pressure between an unusual pair of parallel plates at finite temperature,
namely: a perfectly conducting plate and an infinitely permeable one. The high
and low temperature limits of these quantities are discussed; relationships
between high and low temperature limits are estabkished by means of a modified
version of the temperature inversion symmetry.Comment: latex file 9 pages, 3 figure
Effective potential and stability of the rigid membrane
The calculation of the effective potential for fixed-end and toroidal rigid
-branes is performed in the one-loop as well as in the approximations.
The analysis of the involved zeta-functions (of inhomogeneous Epstein type)
which appear in the process of regularization is done in full detail.
Assymptotic formulas (allowing only for exponentially decreasing errors of
order ) are found which carry all the dependences on the basic
parameters of the theory explicitly. The behaviour of the effective potential
(specified to the membrane case ) is investigated, and the extrema of this
effective potential are obtained.Comment: 15 PAGE
Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity
From the beginning of the subject, calculations of quantum vacuum energies or
Casimir energies have been plagued with two types of divergences: The total
energy, which may be thought of as some sort of regularization of the
zero-point energy, , seems manifestly divergent. And
local energy densities, obtained from the vacuum expectation value of the
energy-momentum tensor, , typically diverge near
boundaries. The energy of interaction between distinct rigid bodies of whatever
type is finite, corresponding to observable forces and torques between the
bodies, which can be unambiguously calculated. The self-energy of a body is
less well-defined, and suffers divergences which may or may not be removable.
Some examples where a unique total self-stress may be evaluated include the
perfectly conducting spherical shell first considered by Boyer, a perfectly
conducting cylindrical shell, and dilute dielectric balls and cylinders. In
these cases the finite part is unique, yet there are divergent contributions
which may be subsumed in some sort of renormalization of physical parameters.
The divergences that occur in the local energy-momentum tensor near surfaces
are distinct from the divergences in the total energy, which are often
associated with energy located exactly on the surfaces. However, the local
energy-momentum tensor couples to gravity, so what is the significance of
infinite quantities here? For the classic situation of parallel plates there
are indications that the divergences in the local energy density are consistent
with divergences in Einstein's equations; correspondingly, it has been shown
that divergences in the total Casimir energy serve to precisely renormalize the
masses of the plates, in accordance with the equivalence principle.Comment: 53 pages, 1 figure, invited review paper to Lecture Notes in Physics
volume in Casimir physics edited by Diego Dalvit, Peter Milonni, David
Roberts, and Felipe da Ros
Casimir Effect on the Worldline
We develop a method to compute the Casimir effect for arbitrary geometries.
The method is based on the string-inspired worldline approach to quantum field
theory and its numerical realization with Monte-Carlo techniques. Concentrating
on Casimir forces between rigid bodies induced by a fluctuating scalar field,
we test our method with the parallel-plate configuration. For the
experimentally relevant sphere-plate configuration, we study curvature effects
quantitatively and perform a comparison with the ``proximity force
approximation'', which is the standard approximation technique. Sizable
curvature effects are found for a distance-to-curvature-radius ratio of a/R >~
0.02. Our method is embedded in renormalizable quantum field theory with a
controlled treatment of the UV divergencies. As a technical by-product, we
develop various efficient algorithms for generating closed-loop ensembles with
Gaussian distribution.Comment: 27 pages, 10 figures, Sect. 2.1 more self-contained, improved data
for Fig. 6, minor corrections, new Refs, version to be published in JHE
Thermal Casimir effect in ideal metal rectangular boxes
The thermal Casimir effect in ideal metal rectangular boxes is considered
using the method of zeta functional regularization. The renormalization
procedure is suggested which provides the finite expression for the Casimir
free energy in any restricted quantization volume. This expression satisfies
the classical limit at high temperature and leads to zero thermal Casimir force
for systems with infinite characteristic dimensions. In the case of two
parallel ideal metal planes the results, as derived previously using thermal
quantum field theory in Matsubara formulation and other methods, are reproduced
starting from the obtained expression. It is shown that for rectangular boxes
the temperature-dependent contribution to the electromagnetic Casimir force can
be both positive and negative depending on side lengths. The numerical
computations of the scalar and electromagnetic Casimir free energy and force
are performed for cubesComment: 10 pages, 4 figures, to appear in Europ. Phys. J.
Calculating Casimir Energies in Renormalizable Quantum Field Theory
Quantum vacuum energy has been known to have observable consequences since
1948 when Casimir calculated the force of attraction between parallel uncharged
plates, a phenomenon confirmed experimentally with ever increasing precision.
Casimir himself suggested that a similar attractive self-stress existed for a
conducting spherical shell, but Boyer obtained a repulsive stress. Other
geometries and higher dimensions have been considered over the years. Local
effects, and divergences associated with surfaces and edges have been studied
by several authors. Quite recently, Graham et al. have re-examined such
calculations, using conventional techniques of perturbative quantum field
theory to remove divergences, and have suggested that previous self-stress
results may be suspect. Here we show that the examples considered in their work
are misleading; in particular, it is well-known that in two dimensions a
circular boundary has a divergence in the Casimir energy for massless fields,
while for general dimension not equal to an even integer the corresponding
Casimir energy arising from massless fields interior and exterior to a
hyperspherical shell is finite. It has also long been recognized that the
Casimir energy for massive fields is divergent for . These conclusions
are reinforced by a calculation of the relevant leading Feynman diagram in
and three dimensions. There is therefore no doubt of the validity of the
conventional finite Casimir calculations.Comment: 25 pages, REVTeX4, 1 ps figure. Revision includes new subsection 4B
and Appendix, and other minor correction
Non-Abelian Vortices in Supersymmetric Gauge Field Theory via Direct Methods
Vortices in supersymmetric gauge field theory are important constructs in a
basic conceptual phenomenon commonly referred to as the dual Meissner effect
which is responsible for color confinement. Based on a direct minimization
approach, we present a series of sharp existence and uniqueness theorems for
the solutions of some non-Abelian vortex equations governing color-charged
multiply distributed flux tubes, which provide an essential mechanism for
linear confinement. Over a doubly periodic domain, existence results are
obtained under explicitly stated necessary and sufficient conditions that
relate the size of the domain, the vortex numbers, and the underlying physical
coupling parameters of the models. Over the full plane, existence results are
valid for arbitrary vortex numbers and coupling parameters. In all cases,
solutions are unique.Comment: 38 pages, late