1,010 research outputs found
Gauged NJL model at strong curvature
We investigate the gauged NJL--model in curved spacetime using the RG
formulation and the equivalency with the gauge Higgs--Yukawa model in a
modified 1/N_c -expansion. The strong curvature induced chiral symmetry
breaking is found in the non-perturbative RG approach (presumably equivalent to
the ladder Schwinger--Dyson equations). Dynamically generated fermion mass is
explicitly calculated and inducing of Einstein gravity is briefly discussed.
This approach shows the way to the non-perturbative study of the dynamical
symmetry breaking at external fields
On the issue of imposing boundary conditions on quantum fields
An interesting example of the deep interrelation between Physics and
Mathematics is obtained when trying to impose mathematical boundary conditions
on physical quantum fields. This procedure has recently been re-examined with
care. Comments on that and previous analysis are here provided, together with
considerations on the results of the purely mathematical zeta-function method,
in an attempt at clarifying the issue. Hadamard regularization is invoked in
order to fill the gap between the infinities appearing in the QFT renormalized
results and the finite values obtained in the literature with other procedures.Comment: 13 pages, no figure
Forbidden patterns and shift systems
The scope of this paper is two-fold. First, to present to the researchers in
combinatorics an interesting implementation of permutations avoiding
generalized patterns in the framework of discrete-time dynamical systems.
Indeed, the orbits generated by piecewise monotone maps on one-dimensional
intervals have forbidden order patterns, i.e., order patterns that do not occur
in any orbit. The allowed patterns are then those patterns avoiding the
so-called forbidden root patterns and their shifted patterns. The second scope
is to study forbidden patterns in shift systems, which are universal models in
information theory, dynamical systems and stochastic processes. Due to its
simple structure, shift systems are accessible to a more detailed analysis and,
at the same time, exhibit all important properties of low-dimensional chaotic
dynamical systems (e.g., sensitivity to initial conditions, strong mixing and a
dense set of periodic points), allowing to export the results to other
dynamical systems via order-isomorphisms.Comment: 21 pages, expanded Section 5 and corrected Propositions 3 and
The Casimir Effect for Generalized Piston Geometries
In this paper we study the Casimir energy and force for generalized pistons
constructed from warped product manifolds of the type where
is an interval of the real line and is a smooth compact
Riemannian manifold either with or without boundary. The piston geometry is
obtained by dividing the warped product manifold into two regions separated by
the cross section positioned at . By exploiting zeta function
regularization techniques we provide formulas for the Casimir energy and force
involving the arbitrary warping function and base manifold .Comment: 16 pages, LaTeX. To appear in the proceedings of the Conference on
Quantum Field Theory Under the Influence of External Conditions (QFEXT11).
Benasque, Spain, September 18-24, 201
Thermodynamic Properties of the Piecewise Uniform String
The thermodynamic free energy F is calculated for a gas whose particles are
the quantum excitations of a piecewise uniform bosonic string. The string
consists of two parts of length L_I and L_II, endowed with different tensions
and mass densities, adjusted in such a way that the velocity of sound always
equals the velocity of light. The explicit calculation is done under the
restrictive condition that the tension ratio x = T_I/T_II approaches zero.
Also, the length ratio s = L_II/L_I is assumed to be an integer. The expression
for F is given on an integral form, in which s is present as a parameter. For
large values of s, the Hagedorn temperature becomes proportional to the square
root of s.Comment: 32 pages, latex, no figure
Dynamical Casimir Effect with Semi-Transparent Mirrors, and Cosmology
After reviewing some essential features of the Casimir effect and,
specifically, of its regularization by zeta function and Hadamard methods, we
consider the dynamical Casimir effect (or Fulling-Davis theory), where related
regularization problems appear, with a view to an experimental verification of
this theory. We finish with a discussion of the possible contribution of vacuum
fluctuations to dark energy, in a Casimir like fashion, that might involve the
dynamical version.Comment: 11 pages, Talk given in the Workshop ``Quantum Field Theory under the
Influence of External Conditions (QFEXT07)'', Leipzig (Germany), September 17
- 21, 200
Explicit Zeta Functions for Bosonic and Fermionic Fields on a Noncommutative Toroidal Spacetime
Explicit formulas for the zeta functions corresponding to
bosonic () and to fermionic () quantum fields living on a
noncommutative, partially toroidal spacetime are derived. Formulas for the most
general case of the zeta function associated to a quadratic+linear+constant
form (in {\bf Z}) are obtained. They provide the analytical continuation of the
zeta functions in question to the whole complex plane, in terms of series
of Bessel functions (of fast, exponential convergence), thus being extended
Chowla-Selberg formulas. As well known, this is the most convenient expression
that can be found for the analytical continuation of a zeta function, in
particular, the residua of the poles and their finite parts are explicitly
given there. An important novelty is the fact that simple poles show up at
, as well as in other places (simple or double, depending on the number of
compactified, noncompactified, and noncommutative dimensions of the spacetime),
where they had never appeared before. This poses a challenge to the
zeta-function regularization procedure.Comment: 15 pages, no figures, LaTeX fil
Nonabelian solutions in AdS_4 and d=11 supergravity
We consider solutions of the four dimensional Einstein-Yang-Mills system with
a negative cosmological constant , where is the nonabelian
gauge coupling constant. This theory corresponds to a consistent truncation of
gauged supergravity and may be uplifted to supergravity. A
systematic study of all known solutions is presented as well as new
configurations corresponding to rotating regular dyons and rotating nonabelian
black holes. The thermodynamics of the static black hole solutions is also
discussed. The generic EYM solutions present a nonvanishing magnetic flux at
infinity and should give us information about the structure of a CFT in a
background SU(2) field. We argue that the existence of these configurations
violating the no hair conjecture is puzzling from the AdS/CFT point of view.Comment: 52 pages; 24 figures; v2: minor changes, references added, version to
be published in PR
Casimir effect in de Sitter and Anti-de Sitter braneworlds
We discuss the bulk Casimir effect (effective potential) for a conformal or
massive scalar when the bulk represents five-dimensional AdS or dS space with
two or one four-dimensional dS brane, which may correspond to our universe.
Using zeta-regularization, the interesting conclusion is reached, that for both
bulks in the one-brane limit the effective potential corresponding to the
massive or to the conformal scalar is zero. The radion potential in the
presence of quantum corrections is found. It is demonstrated that both the dS
and the AdS braneworlds may be stabilized by using the Casimir force only. A
brief study indicates that bulk quantum effects are relevant for brane
cosmology, because they do deform the de Sitter brane. They may also provide a
natural mechanism yielding a decrease of the four-dimensional cosmological
constant on the physical brane of the two-brane configuration.Comment: 37 pages, LaTeX, references added, some revision is done, version to
appear in PR
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