arXiv subjects

E. Elizalde

Publications and source records attributed to E. Elizalde.

At least 109 records · Page 6Linked to original sources

arXiv1998

Non-Gaussian bounds in the variance from small scale CMB observations

We compare the latest results from CMB experiments at scales around $l_e \sim 150$ over different parts of the sky to test the hypothesis that they are drawn from a Gaussian distribution, as is usually assumed. Using both the diagonal and the full covariance $χ^2$ test, we compare the data with different sets of strategies and find in all cases incompatibility with the Gaussian hypothesis above the one-sigma level. We next show how to include a generic non-Gaussian signal in the data analysis. Results from CMB observations can be made compatible with each other by assuming a non-Gaussian distribution for the signal, with a kurtosis at a level $B_4 = <{δ_T^4}>_c /{<{δ_T^2}>_c}^2 \simeq 90$. A possible interpretation for this result is that the initial fluctuations at the surface of last scattering are strongly non-Gaussian. Another interpretation is that the systematic errors have been understimated in all observations by a factor of two. Other explanations include foreground contamination, non-linear effects or a combination of them.

astro-ph↗

arXiv1997

Zeta-function regularization, the multiplicative anomaly and the Wodzicki residue

The multiplicative anomaly associated with the zeta-function regularized determinant is computed for the Laplace-type operators $L_1=-\lap+V_1$ and $L_2=-\lap+V_2$, with $V_1$, $V_2$ constant, in a D-dimensional compact smooth manifold $ M_D$, making use of several results due to Wodzicki and by direct calculations in some explicit examples. It is found that the multiplicative anomaly is vanishing for $D$ odd and for D=2. An application to the one-loop effective potential of the O(2) self-interacting scalar model is outlined.

hep-th↗

arXiv1997

Multidimensional extension of the generalized Chowla-Selberg formula

After recalling the precise existence conditions of the zeta function of a pseudodifferential operator, and the concept of reflection formula, an exponentially convergent expression for the analytic continuation of a multidimensional inhomogeneous Epstein-type zeta function of the general form ζ_{A,\vec{b},q} (s) = \sum_{\vec{n}\in Z^p (\vec{n}^T A \vec{n} +\vec{b}^T \vec{n}+q)^{-s}, with $A$ the $p\times p$ matrix of a quadratic form, $\vec{b}$ a $p$ vector and $q$ a constant, is obtained. It is valid on the whole complex $s$-plane, is exponentially convergent and provides the residua at the poles explicitly. It reduces to the famous formula of Chowla and Selberg in the particular case $p=2$, $\vec{b}= \vec{0}$, $q=0$. Some variations of the formula and physical applications are considered.

hep-th↗

arXiv1997

Casimir energy in the MIT bag model

The vacuum energies corresponding to massive Dirac fields with the boundary conditions of the MIT bag model are obtained. The calculations are done with the fields occupying the regions inside and outside the bag, separately. The renormalization procedure for each of the situations is studied in detail, in particular the differences occurring with respect to the case when the field extends over the whole space. The final result contains several constants undergoing renormalization, which can be determined only experimentally. The non-trivial finite parts which appear in the massive case are found exactly, providing a precise determination of the complete, renormalized zero-point energy for the first time, in the fermionic case. The vacuum energy behaves like inverse powers of the mass for large masses.

hep-th↗

arXiv1996

Complete determination of the singularity structure of zeta functions

Series of extended Epstein type provide examples of non-trivial zeta functions with important physical applications. The regular part of their analytic continuation is seen to be a convergent or an asymptotic series. Their singularity structure is completely determined in terms of the Wodzicki residue in its generalized form, which is proven to yield the residua of all the poles of the zeta function, and not just that of the rightmost pole (obtainable from the Dixmier trace). The calculation is a very down-to-earth application of these powerful functional analytical methods in physics.

hep-th↗

arXiv1996

Casimir energies for massive fields in the bag

The Casimir energy corresponding to a massive scalar field with Dirichlet boundary conditions on a spherical bag is obtained. The field is considered, separately, inside and outside the bag. The renormalization procedure that is necessary to apply in each situation is studied in detail, in particular the differences occurring with respect to the case when the field occupies the whole space. The final result contains several constants that experience renormalization and can be determined only experimentally. The non-trivial finite parts that appear in the massive case are found exactly, providing a precise determination of the complete, renormalized zero-point energy for the first time.

hep-th↗

arXiv1996

The Gross-Neveu model on a sphere with a magnetic monopole

We study, for the first time, the phase structure of the Gross--Neveu model with a combination of a (constant) gravitational and a magnetic field. This has been made possible by our finding of an exact solution to the problem, namely the effective potential for the composite fermions. Then, from the corresponding implicit equation the phase diagram for the dynamical fermion mass is calculated numerically for some values of the magnetic field. %(what can be done with arbitrary precision). For a small magnetic field the phase diagram hints to the possibility of a second order phase transition at some critical curvature. With growing magnetic field only the phase with broken chiral symmetry survives, because the magnetic field prevents the decay of the chiral condensate. This result is bound to have important consequences in early universe cosmology.

hep-th↗

arXiv1996

Zeta function for the Laplace operator acting on forms in a ball with gauge boundary conditions

The Laplace operator acting on antisymmetric tensor fields in a $D$--dimensional Euclidean ball is studied. Gauge-invariant local boundary conditions (absolute and relative ones, in the language of Gilkey) are considered. The eigenfuctions of the operator are found explicitly for all values of $D$. Using in a row a number of basic techniques, as Mellin transforms, deformation and shifting of the complex integration contour, and pole compensation, the zeta function of the operator is obtained. From its expression, in particular, $ζ(0)$ and $ζ'(0)$ are evaluated exactly. A table is given in the paper for $D=3, 4, ...,8$. The functional determinants and Casimir energies are obtained for $D=3, 4, ...,6$.

hep-th↗

arXiv1996

Antisymmetric tensor fields on spheres: functional determinants and non--local counterterms

The Hodge--de Rham Laplacian on spheres acting on antisymmetric tensor fields is considered. Explicit expressions for the spectrum are derived in a quite direct way, confirming previous results. Associated functional determinants and the heat kernel expansion are evaluated. Using this method, new non--local counterterms in the quantum effective action are obtained, which can be expressed in terms of Betti numbers.

hep-th↗

arXiv1996

The renormalization group and spontaneous compactification of a higher-dimensional scalar field theory in curved spacetime

The renormalization group (RG) is used to study the asymptotically free $ϕ_6^3$-theory in curved spacetime. Several forms of the RG equations for the effective potential are formulated. By solving these equations we obtain the one-loop effective potential as well as its explicit forms in the case of strong gravitational fields and strong scalar fields. Using zeta function techniques, the one-loop and corresponding RG improved vacuum energies are found for the Kaluza-Klein backgrounds $R^4\times S^1\times S^1$ and $R^4\times S^2$. They are given in terms of exponentially convergent series, appropriate for numerical calculations. A study of these vacuum energies as a function of compactification lengths and other couplings shows that spontaneous compactification can be qualitatively different when the RG improved energy is used.

hep-th↗

arXiv1995

Quantum effects of stringy and membranic nature for the swimming of micro-organisms in a fluid

The static potential is investigated in string and membrane theories coupled to $U(1)$ gauge fields (specifically, external magnetic fields) and with antisymmetric tensor fields. The explicit dependence of the potential on the shape of the extended objects is obtained, including a careful calculation of the quantum effects. Noting the features which are common to the dynamics of strings and membranes moving in background fields and to the swimming of micro-organisms in a fluid, the latter problem is studied. The Casimir energy of a micro-organism is estimated, taking into account the quantum effects and the backreaction from the outside fluid. The static potential is investigated in string and membrane theories coupled to $U(1)$ gauge fields (specifically, external magnetic fields) and with antisymmetric tensor fields. The explicit dependence of the potential on the shape of the extended objects is obtained, including a careful calculation of the quantum effects. Noting the features which are common to the dynamics of strings and membranes moving in background fields and to the swimming of micro-organisms in a fluid, the latter problem is studied. The Casimir energy of a micro-organism is estimated, taking into account the quantum effects and the backreaction from the outside fluid.

hep-th↗

arXiv1995

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.

hep-th↗

arXiv1995

Dilatonic gravity near two dimensions as a string theory

Using the renormalization-group formalism, a sigma model of a special type- in which the metric and the dilaton depend explicitly on one of the string coordinates only-is investigated near two dimensions. It is seen that dilatonic gravity coupled to N scalar fields can be expressed in this form, using a string parametrization, and that it possesses the usual UV fixed point. However,in this stringy parametrization of the theory the fixed point for the scalar-dilaton coupling turns out to be trivial, while the fixed point for the gravitational coupling remains to be the same as in previous studies being, in particular, non-trivial.

hep-th↗

arXiv1995

Casimir energy of a massive field in a genus-1 surface

We review the definition of the Casimir energy steming naturally from the concept of functional determinant through the zeta function prescription. This is done by considering the theory at finite temperature and by defining then the Casimir energy as its energy in the limit $T\to 0$. The ambiguity in the coefficient $C_{d/2}$ is understood to be a result of the necessary renormalization of the free energy of the system. Then, as an exact, explicit example never calculated before, the Casimir energy for a massive scalar field living in a general $(1+2)$-dimensional toroidal spacetime (i.e., a general surface of genus one) with flat spatial geometry ---parametrized by the corresponding Teichmüller parameters--- and its precise dependence on these parameters and on the mass of the field is obtained under the form of an analytic function.

hep-th↗

arXiv1995

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.

hep-th↗

arXiv1995

A renormalization group improved non-local gravitational effective Lagrangian

Renormalization group techniques are used in order to obtain the improved non-local gravitational effective action corresponding to any asymptotically free GUT, up to invariants which are quadratic on the curvature. The corresponding non-local gravitational equations are written down, both for the case of asymptotically free GUTs and also for quantum R$^2$-gravity. The implications of the results when obtaining the flux of vacuum radiation through the future null infinity are briefly discussed.

gr-qc↗

arXiv1995

Bosonic string with antisymmetric fields and a non-local Casimir effect

The coupling, in a non-standard way, of a bosonic string theory with a dilaton and antisymmetric fields is investigated. By integrating over the antisymmetric fields, a Coulomb-like interaction term is generated. The static potential of a theory of this kind is obtained from the corresponding non-local zeta function, in some approximation. An interpretation of the static potential as a type of non-local Casimir effect is given.

hep-th↗

arXiv1995

The conformal anomaly in N-dimensional space having a hyperbolic spatial section

The conformal anomaly for spinors and scalars on a N-dimensional hyperbolic space is calculated explicitly, by using zeta-function regularization techniques and the Selberg trace formula. In the case of conformally invariant spinors and scalars the results are very much related with those corresponding to a N-dimensional sphere.

gr-qc↗