234 research outputs found
Casimir Theory of the Relativistic Composite String Revisited, and a Formally Related Problem in Scalar QFT
The main part of this paper is to present an updated review of the Casimir
energy at zero and finite temperature for the transverse oscillations of a
piecewise uniform closed string. We make use of three different
regularizations: the cutoff method, the complex contour integration method, and
the zeta-function method. The string model is relativistic, in the sense that
the velocity of sound is for each string piece set equal to the velocity of
light. In this sense the theory is analogous to the electromagnetic theory in a
dielectric medium in which the product of permittivity and permeability is
equal to unity (an isorefractive medium). We demonstrate how the formalism
works for a two-piece string, and for a 2N-piece string, and show how in the
latter case a compact recursion relation serves to facilitate the formalism
considerably. The Casimir energy turns out to be negative, and the more so the
larger the number of pieces in the string. The two-piece string is quantized in
D-dimensional spacetime, in the limit when the ratio between the two tensions
is very small. We calculate the free energy and other thermodynamic quantities,
demonstrate scaling properties, and comment on the meaning of the Hagedorn
critical temperature for the two-piece string. Thereafter, as a novel
development we present a scalar field theory for a real field in
three-dimensional space in a potential rising linearly with a longitudinal
coordinate z in the interval 0<z<1, and which is thereafter held constant on a
horizontal plateau. The potential is taken as a rough model of the two-piece
string potential under simplifying conditions, when the length ratio between
the pieces is replaced formally with the mentioned length parameter z.Comment: 24 latex pages, one figure. Contribution to the honorary issue of J.
Phys. A, on the occasion of the 75th anniversary of Professor Stuart Dowker.
The present version, augmented by a section on a related one-dimensional
problem in scalar QFT, matches the forthcoming published versio
Viscous Cosmology and the Cardy-Verlinde Formula
The holographic principle in a radiation dominated universe is extended to
incorporate the case of a bulk-viscous cosmic fluid. This corresponds to a
nonconformally invariant theory. Generalization of the Cardy-Verlinde entropy
formula to the viscous case appears to be possible from a formal point of view,
although we question on physical grounds the manner in which the Casimir energy
is evaluated in this case. Also, we consider an observation recently made by
Youm, namely that the entropy of the universe is no longer expressible in the
conventional Cardy-Verlinde form if one relaxes the radiation dominance
equation of state and instead merely assumes that the pressure is proportional
to the energy density. We show that Youm's generalized entropy formula remains
valid when the cosmic fluid is no longer ideal, but endowed with a constant
bulk viscosity.Comment: 10 pages, no figures. Contribution to the Proceedings of the Second
Londrina Winter School "Mathematical Methods in Physics", August 25-30, 2002,
Londrina-Parana, Brazi
Viscosity-Induced Crossing of the Phantom Divide in the Dark Cosmic Fluid
Choosing various natural forms for the equation-of-state parameter w and the
bulk viscosity \zeta, we discuss how it is possible for a dark energy fluid to
slide from the quintessence region across the divide w=-1 into the phantom
region, and thus into a Big Rip future singularity. Different analytic forms
for \zeta, as powers of the scalar expansion, are suggested and compared with
experiments.Comment: 11 pages latex, no figure
Viscosity-Induced Crossing of the Phantom Barrier
We show explicitly, by using astrophysical data plus reasonable assumptions
for the bulk viscosity in the cosmic fluid, how the magnitude of this viscosity
may be high enough to drive the fluid from its position in the quintessence
region at present time across the barrier into the phantom region
in the late universe. The phantom barrier is accordingly not a sharp
mathematical divide, but rather a fuzzy concept. We also calculate the limiting
forms of various thermodynamical quantities, including the rate of entropy
production, for a dark energy fluid near the future Big Rip singularity.Comment: 11 pages, latex, no figures, to appear in Entrop
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