arXiv subjects
Publications and source records attributed to Enrique Álvarez.
The only allowed source of the gravitational field in the unimodular theory, invariant under area-preserving (transverse) diffeomorphisms as well as Weyl transformations, is just the traceless piece of the energy-momentum tensor. This fact notwithstanding, the free energy produced by arbitrary sources (not only static ones) is identical to the one predicted by general relativity. This encompasses all weak field tests of gravitation.
The approximate late conformal time wavefunctional for self-interacting scalar quantum fields in Friedmann-Robertson-Walker spaces is computed. It is a good candidate for the {\em vacuum wavefunctional} in such spaces.
The problem of the vacuum energy decay is studied through the analysis of the vacuum survival amplitude ${\mathcal A}(z, z')$. Transition amplitudes are computed for finite time-span, $Z\equiv z^\prime-z$, and their {\em late time} behavior is discussed up to first order in the coupling constant, $ł$.
The problem of the vacuum energy decay is studied for both signs of the cosmological constant, through the analysis of the vacuum survival amplitude, defined in terms of the {\em conformal time}, $z$, by ${\mathcal A}(z,z^\prime)\equiv <\text{vac}\,z|\text{vac}\,z^\prime>$. Transition amplitudes are computed for finite time-span, $Z\equiv z^\prime-z$, and their {\em late time} behavior (directly related to the putative decay width of the state) as well as the transients are discussed up to first order in the coupling constant, $λ$.
The {\em instability of vacuum energy} in de Sitter space as discussed recently by Polyakov is argued to be a generic feature when external gravitational fields are present. It is related to the existence of {\em forbidden} (by momentum conservation) decays derived in some detail by Bros, Epstein and Moschella. Some calculations are discussed in a conformally invariant setting, and a flat space model is presented.
Scale invariant (transverse) gravitational theories are introduced. They are invariant under pure metric rescalings (i.e. the matter fields are inert under those). This symmetry forbids the presence of a cosmological constant. Those theories are not invariant under the full set of diffeomorphisms, but only with respect to those locally characterized by the fact that their generator is transverse $\pd_\a ξ^\a=0$.
The purpose of this paper is to analyze the stability of interacting matter in the presence of a cosmological constant. Using an approach based on the heat equation, no imaginary part is found for the effective potential in the presence of a fixed background, which is the n-dimensional sphere or else an analytical continuation thereof, which is explored in some detail.
Theories of gravity invariant under those diffeomorphisms generated by transverse vectors, $\pd_\mξ^\m=0$ are considered. Such theories are dubbed transverse, and differ from General Relativity in that the determinant of the metric, $g$, is a transverse scalar. We comment on diverse ways in which these models can be constrained using a variety of observations. Generically, an additional scalar degree of freedom mediates the interaction, so the usual constraints on scalar-tensor theories have to be imposed. If the purely gravitational part is Einstein--Hilbert but the matter action is transverse, the models predict that the three {\em a priori} different concepts of mass (gravitational active and gravitational passive as well as inertial) are not equivalent anymore. These transverse deviations from General Relativity are therefore tightly constrained, actually correlated with existing bounds on violations of the equivalence principle, local violations of Newton's third law and/or violation of Local Position Invariance.
The effects of a non-vanishing value for the cosmological constant in the scenario of Lorentz symmetry breaking recently proposed by Cohen and Glashow (which they denote as Very Special Relativity) are explored and observable consequences are pointed out.
Some models are presented in which the strength of the gravitational coupling of the potential energy relative to the same coupling for the kinetic energy is, in a precise sense, adjustable. The gauge symmetry of these models consists of those coordinate changes with unit jacobian.
Several ways of computing the radiative corrections to the heavy boson masses in Kaluza-Klein theory are discussed. It is argued that only an intrinsically higher dimensional approach embodies all the desired physical properties.
This is a non-technical summary of the subtleties of quantum corrections on extra-dimensional theories: should one first renormalize and then mode expand, or first expand in four-dimensional modes and then renormalize?
Using six-dimensional quantum electrodynamics ($QED_6$) as an example we study the one-loop renormalization of the theory both from the six and four-dimensional points of view. Our main conclusion is that the properly renormalized four dimensional theory never forgets its higher dimensional origin. In particular, the coefficients of the neccessary extra counterterms in the four dimensional theory are determined in a precise way. We check our results by studying the reduction of $QED_4$ on a two-torus.
The contents of this paper have been incorporated in the new version of hep-th/0602150.
A general study of non-abelian duality is presented. We first identify a possible obstruction to the conformal invariance of the dual theory for non-semisimple groups. We construct the exact non-abelian dual for any Wess-Zumino-Witten (WZW) model for any anomaly free subgroup, and the corresponding extension for coset conformal field theories. We characterize the exact non-abelian dual for $σ$-models with chiral isometries and extend the standard notion of duality to anomalous subgroups of WZW models, thus giving a way of constructing dual transformations for different groups on the left and on the right. We also present some new examples of non-abelian duality for four-dimensional gravitational instantons.
Two-dimensional sigma models in curved target spaces are considered in which a relationship between the warp factor and the dilaton is imposed in a renormalization group invariant way.
Two popular attempts to understand the quantum physics of gravitation are critically assessed. The talk on which this paper is based was intended for a general particle-physics audience.