142 research outputs found
Applications of the Mellin-Barnes integral representation
We apply the Mellin-Barnes integral representation to several situations of
interest in mathematical-physics. At the purely mathematical level, we derive
useful asymptotic expansions of different zeta-functions and partition
functions. These results are then employed in different topics of quantum field
theory, which include the high-temperature expansion of the free energy of a
scalar field in ultrastatic curved spacetime, the asymptotics of the -brane
density of states, and an explicit approach to the asymptotics of the
determinants that appear in string theory.Comment: 20 pages, LaTe
Local Casimir Energies for a Thin Spherical Shell
The local Casimir energy density for a massless scalar field associated with
step-function potentials in a 3+1 dimensional spherical geometry is considered.
The potential is chosen to be zero except in a shell of thickness ,
where it has height , with the constraint . In the limit of zero
thickness, an ideal -function shell is recovered. The behavior of the
energy density as the surface of the shell is approached is studied in both the
strong and weak coupling regimes. The former case corresponds to the well-known
Dirichlet shell limit. New results, which shed light on the nature of surface
divergences and on the energy contained within the shell, are obtained in the
weak coupling limit, and for a shell of finite thickness. In the case of zero
thickness, the energy has a contribution not only from the local energy
density, but from an energy term residing entirely on the surface. It is shown
that the latter coincides with the integrated local energy density within the
shell. We also study the dependence of local and global quantities on the
conformal parameter. In particular new insight is provided on the reason for
the divergence in the global Casimir energy in third order in the coupling.Comment: 16 pages, revtex 4, no figures. Major additions, clarifications, and
corections, references adde
Topology in 2D CP**(N-1) models on the lattice: a critical comparison of different cooling techniques
Two-dimensional CP**(N-1) models are used to compare the behavior of
different cooling techniques on the lattice. Cooling is one of the most
frequently used tools to study on the lattice the topological properties of the
vacuum of a field theory. We show that different cooling methods behave in an
equivalent way. To see this we apply the cooling methods on classical
instantonic configurations and on configurations of the thermal equilibrium
ensemble. We also calculate the topological susceptibility by using the cooling
technique.Comment: 24 pages, 10 figures (from 16 eps files
The heat kernel for deformed spheres
We derive the asymptotic expansion of the heat kernel for a Laplace operator
acting on deformed spheres. We calculate the coefficients of the heat kernel
expansion on two- and three-dimensional deformed spheres as functions of
deformation parameters. We find that under some deformation the conformal
anomaly for free scalar fields on and is canceled.Comment: 10 pages, latex, no figure
Zero-point energy of massless scalar fields in the presence of soft and semihard boundaries in D dimensions
The renormalized energy density of a massless scalar field defined in a
D-dimensional flat spacetime is computed in the presence of "soft" and
"semihard" boundaries, modeled by some smoothly increasing potential functions.
The sign of the renormalized energy densities for these different confining
situations is investigated. The dependence of this energy on for the cases
of "hard" and "soft/semihard" boundaries are compared.Comment: 36 pages, LaTeX, 4 figure
Phenomenological Equations of State for the Quark-Gluon Plasma
Two phenomenological models describing an SU(N) quark-gluon plasma are
presented. The first is obtained from high temperature expansions of the free
energy of a massive gluon, while the second is derived by demanding color
neutrality over a certain length scale. Each model has a single free parameter,
exhibits behavior similar to lattice simulations over the range T_d - 5T_d, and
has the correct blackbody behavior for large temperatures. The N = 2
deconfinement transition is second order in both models, while N = 3,4, and 5
are first order. Both models appear to have a smooth large-N limit. For N >= 4,
it is shown that the trace of the Polyakov loop is insufficient to characterize
the phase structure; the free energy is best described using the eigenvalues of
the Polyakov loop. In both models, the confined phase is characterized by a
mutual repulsion of Polyakov loop eigenvalues that makes the Polyakov loop
expectation value zero. In the deconfined phase, the rotation of the
eigenvalues in the complex plane towards 1 is responsible for the approach to
the blackbody limit over the range T_d - 5T_d. The addition of massless quarks
in SU(3) breaks Z(3) symmetry weakly and eliminates the deconfining phase
transition. In contrast, a first-order phase transition persists with
sufficiently heavy quarks.Comment: 22 pages, RevTeX, 9 eps file
Finite Temperature and Density Effect on Symmetry Breaking by Wilson Loops
A finite temperature and density effect of Wilson loop elements on non-simply
connected space is investigated in the model suggested by Hosotani. Using
one-loop calculations it is shown that the value of an "order parameter" does
not shift as the temperature grows. We find that finite density effect is of
much importance for restoration of symmetry.Comment: 11pages, no figur
Surface Divergences and Boundary Energies in the Casimir Effect
Although Casimir, or quantum vacuum, forces between distinct bodies, or
self-stresses of individual bodies, have been calculated by a variety of
different methods since 1948, they have always been plagued by divergences.
Some of these divergences are associated with the volume, and so may be more or
less unambiguously removed, while other divergences are associated with the
surface. The interpretation of these has been quite controversial. Particularly
mysterious is the contradiction between finite total self-energies and surface
divergences in the local energy density. In this paper we clarify the role of
surface divergences.Comment: 8 pages, 1 figure, submitted to proceedings of QFEXT0
Fluctuations of quantum fields via zeta function regularization
Explicit expressions for the expectation values and the variances of some
observables, which are bilinear quantities in the quantum fields on a
D-dimensional manifold, are derived making use of zeta function regularization.
It is found that the variance, related to the second functional variation of
the effective action, requires a further regularization and that the relative
regularized variance turns out to be 2/N, where N is the number of the fields,
thus being independent on the dimension D. Some illustrating examples are
worked through.Comment: 15 pages, latex, typographical mistakes correcte
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
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