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E. Elizalde

Publications and source records attributed to E. Elizalde.

At least 145 records · Page 8Linked to original sources
arXiv1994

Renormalization-Group Improved Effective Potential for Finite Grand Unified Theories in Curved Spacetime

The renormalization-group improved effective potential ---to leading-log and in the linear curvature approximation--- is constructed for ``finite'' theories in curved spacetime. It is not trivial and displays a quite interesting, exponential-like structure ---in contrast with the case of flat spacetime where it coincides with the classical potential. Several possible cosmological applications, as curvature-induced phase transitions and modifications of the values of the gravitational and cosmological constants, are briefly discussed.

hep-th↗
arXiv1994

One-Loop Renormalization and Asymptotic Behaviour of a Higher-Derivative Scalar Theory in Curved Spacetime

A higher-derivative, interacting, scalar field theory in curved spacetime with the most general action of sigma-model type is studied. The one-loop counterterms of the general theory are found. The renormalization group equations corresponding to two different, multiplicatively renormalizable variants of the same are derived. The analysis of their asymptotic solutions shows that, depending on the sign of one of the coupling constants, we can construct an asymptotically free theory which is also asymptotically conformal invariant at strong (or small) curvature. The connection that can be established between one of the multiplicatively renormalizable variants of the theory and the effective theory of the conformal factor, aiming at the description of quantum gravity at large distances, is investigated.

hep-th↗
arXiv1994

An Extension of the Chowla-Selberg Formula Useful in Quantizing with the Wheeler-De Witt Equation

The two-dimensional inhomogeneous zeta-function series (with homogeneous part of the most general Epstein type): \[ \sum_{m,n \in \mbox{\bf Z}} (am^2+bmn+cn^2+q)^{-s}, \] is analytically continued in the variable $s$ by using zeta-function techniques. A simple formula is obtained, which extends the Chowla-Selberg formula to inhomogeneous Epstein zeta-functions. The new expression is then applied to solve the problem of computing the determinant of the basic differential operator that appears in an attempt at quantizing gravity by using the Wheeler-De Witt equation in 2+1 dimensional spacetime with the torus topology.

hep-th↗
arXiv1994

Possible Evidences of Kaluza-Klein Particles in a Scalar Model with Spherical Compactification

Possible experimental manifestations of the contribution of heavy Kaluza-Klein particles, within a simple scalar model in six dimensions with spherical compactification, are studied. The approach is based on the assumption that the inverse radius $L^{-1}$ of the space of extra dimensions is of the order of the scale of the supersymmetry breaking $M_{SUSY} \sim 1 ÷10$ TeV. The total cross section of the scattering of two light particles is calculated to one loop order and the effect of the Kaluza-Klein tower is shown to be noticeable for energies $\sqrt{s} \geq 1.4 L^{-1}$.

hep-th↗
arXiv1994

Renormalization-Group Improved Effective Potential for Interacting Theories with Several Mass Scales in Curved Spacetime

The renormalization group (RG) is used in order to obtain the RG improved effective potential in curved spacetime. This potential is explicitly calculated for the Yukawa model and for scalar electrodynamics, i.e. theories with several (namely, more than one) mass scales, in a space of constant curvature. Using the $λφ^4$-theory on a general curved spacetime as an example, we show how it is possible to find the RG improved effective Lagrangian in curved spacetime. As specific applications, we discuss the possibility of curvature induced phase transitions in the Yukawa model and the effective equations (back-reaction problem) for the $λφ^4$-theory on a De Sitter background.

hep-th↗
arXiv1994

Chiral Symmetry Breaking in the $d=3$ Nambu-Jona-Lasinio Model in Curved Spacetime

The phase structure of the $d=3$ Nambu-Jona-Lasinio model in curved spacetime is considered to leading order in the $1/N$--expansion and in the linear curvature approximation. The possibility of a curvature-induced first-order phase transition is investigated numerically. The dynamically generated fermionic mass is calculated for some values of the curvature.

hep-th↗
arXiv1993

Chiral Symmetry Breaking in the Nambu-Jona-Lasinio Model in Curved Spacetime with Non-Trivial Topology

We discuss the phase structure (in the $1/N$-expansion) of the Nambu-Jona-Lasinio model in curved spacetime with non-trivial topology ${\cal M}^3 \times {\rm S}^1$. The evaluation of the effective potential of the composite field $\barψ ψ$ is presented in the linear curvature approximation (topology is treated exactly) and in the leading order of the $1/N$-expansion. The combined influence of topology and curvature to the phase transitions is investigated. It is shown, in particular, that at zero curvature and for small radius of the torus there is a second order phase transition from the chiral symmetric to the chiral non-symmetric phase. When the curvature grows and (or) the radius of ${\rm S}^1$ decreases, then the phase transition is in general of first order. The dynamical fermionic mass is also calculated in a number of different situations.

hep-th↗
arXiv1993

Dynamical Determination of the Metric Signature in Spacetime of Nontrivial Topology

The formalism of Greensite for treating the spacetime signature as a dynamical degree of freedom induced by quantum fields is considered for spacetimes with nontrivial topology of the kind ${\bf R}^{D-1} \times {\bf T}^1$, for varying $D$. It is shown that a dynamical origin for the Lorentzian signature is possible in the five-dimensional space ${\bf R}^4 \times {\bf T}^1$ with small torus radius (periodic boundary conditions), as well as in four-dimensional space with trivial topology. Hence, the possibility exists that the early universe might have been of the Kaluza-Klein type, \ie multidimensional and of Lorentzian signature.

hep-th↗
arXiv1993

Renormalization-Group Improved Effective Lagrangian for Interacting Theories in Curved Spacetime

A method for finding the renormalization group (RG) improved effective Lagrangian for a massive interacting field theory in curved spacetime is presented. As a particular example, the $λφ^4$-theory is considered and the RG improved effective Lagrangian is explicitly found up to second order in the curvature tensors. As a further application, the curvature-induced phase transitions are discussed for both the massive and the massless versions of the theory. The problems which appear when calculating the RG improved effective Lagrangian for gauge theories are discussed, taking as example the asymptotically free SU(2) gauge model.

hep-th↗
arXiv1993

One-Loop Renormalization of Higher-Derivative 2D Dilaton Gravity

A theory of higher-derivative 2D dilaton gravity which has its roots in the massive higher-spin mode dynamics of string theory is suggested. The divergences of the effective action to one-loop are calculated, both in the covariant and in the conformal gauge. Some technical problems which appear in the calculations are discussed. An interpretation of the theory as a particular D=2 higher-derivative $σ$-model is given. For a specific case of higher-derivative 2D dilaton gravity, which is one loop multiplicatively renormalizable, static configurations corresponding to black holes are shown to exist.

hep-th↗
arXiv1993

The Vacuum Energy Density for Spherical and Cylindrical Universes

The vacuum energy density (Casimir energy) corresponding to a massless scalar quantum field living in different universes (mainly no-boundary ones), in several dimensions, is calculated. Hawking's zeta function regularization procedure supplemented with a very simple binomial expansion is shown to be a rigorous and well suited method for performing the analysis. It is compared with other, much more involved techniques. The principal-part prescription is used to deal with the poles that eventually appear. Results of the analysis are the absence of poles at four dimensions (for a 4d Riemann sphere and for a 4d cylinder of 3d Riemann spherical section), the total coincidence of the results corresponding to a 3d and a 4d cylinder (the first after pole subtraction), and the fact that the vacuum energy density for cylinders is (in absolute value) over an order of magnitude smaller than for spheres of the same dimension.

hep-th↗
arXiv1993

Zeta-Function Regularization is Uniquely Defined and Well

Hawking's zeta function regularization procedure is shown to be rigorously and uniquely defined, thus putting and end to the spreading lore about different difficulties associated with it. Basic misconceptions, misunderstandings and errors which keep appearing in important scientific journals when dealing with this beautiful regularization method ---and other analytical procedures--- are clarified and corrected.

hep-th↗
arXiv1993

Covariant Effective Action and One-Loop Renormalization of 2D Dilaton Gravity with Fermionic Matter

Two dimensional dilaton gravity interacting with a four-fermion model and scalars is investigated, all the coefficients of the Lagrangian being arbitrary functions of the dilaton field. The one-loop covariant effective action for 2D dilaton gravity with Majorana spinors (including the four-fermion interaction) is obtained, and the technical problems which appear in an attempt at generalizing such calculations to the case of the most general four-fermion model described by Dirac fermions are discussed. A solution to these problems is found, based on its reduction to the Majorana spinor case. The general covariant effective action for 2D dilaton gravity with the four-fermion model described by Dirac spinors is given. The one-loop renormalization of dilaton gravity with Majorana spinors is carried out and the specific conditions for multiplicative renormalizability are found. A comparison with the same theory but with a classical gravitational field is done.

hep-th↗
arXiv1993

Mellin-Barnes Representation for the Genus-g Finite Temperature String Theory

The Mellin-Barnes representation for the free energy of the genus-$g$ string is constructed. It is shown that the interactions of the open bosonic string do not modify the critical (Hagedorn) temperature. However,for the sectors having a spinor structure, the critical temperature exists also for all $g$ and depends on the windings. The appearance of a periodic structure is briefly discussed.

hep-th↗
arXiv1993

The Renormalization Group and the Effective Potential in a Curved Spacetime with Torsion

The renormalization group method is employed to study the effective potential in curved spacetime with torsion. The renormalization-group improved effective potential corresponding to a massless gauge theory in such a spacetime is found and in this way a generalization of Coleman-Weinberg's approach corresponding to flat space is obtained. A method which works with the renormalization group equation for two-loop effective potential calculations in torsionful spacetime is developed. The effective potential for the conformal factor in the conformal dynamics of quantum gravity with torsion is thereby calculated explicitly. Finally, torsion-induced phase transitions are discussed.

hep-th↗
arXiv1993

The Renormalization Structure and Quantum Equivalence of 2D Dilaton Gravities

The one-loop effective action corresponding the general model of dilaton gravity given by the Lagrangian $L=-\sqrt{g} \left[ \frac{1}{2}Z(Φ) g^{μν} \partial_μΦ\partial_νΦ+ C(Φ) R + V (Φ)\right]$, where $Z(Φ)$, $ C(Φ)$ and $V (Φ)$ are arbitrary functions of the dilaton field, is found. The question of the quantum equivalence of classically equivalent dilaton gravities is studied. By specific calculation of explicit examples it is shown that classically equivalent quantum gravities are also perturbatively equivalent at the quantum level, but only on-shell. The renormalization group equations for the generalized effective couplings $Z(Φ)$, $ C(Φ)$ and $V (Φ)$ are written. An analysis of the equations shows, in particular, that the Callan-Giddings-Harvey-Strominger model is not a fixed point of these equations.

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