arXiv subjects
Publications and source records attributed to Ugo Moschella.
We describe a new viewpoint on canonical quantization of linear fields on a general curved background that encompasses and generalizes the standard treatment of canonical QFT given in textbooks. Our method permits the construction of pure states and mixed stated with the same technique. We apply our scheme to the study of Rindler QFT and we present a new derivation of the Unruh effect based on invariance arguments.
We study particle decay in de Sitter space-time as given by first order perturbation theory in a Lagrangian interacting quantum field theory. We study in detail the adiabatic limit of the perturbative amplitude and compute the "phase space" coefficient exactly in the case of two equal particles produced in the disintegration. We show that for fields with masses above a critical mass $m_c$ there is no such thing as particle stability, so that decays forbidden in flat space-time do occur here. The lifetime of such a particle also turns out to be independent of its velocity when that lifetime is comparable with de Sitter radius. Particles with mass lower than critical have a completely different behavior: the masses of their decay products must obey quantification rules, and their lifetime is zero.
We propose a general construction of quantum states for linear canonical quantum fields on a manifold, which encompasses and generalizes the "standard" procedures existing in textbooks. Our method provides pure and mixed states on the same footing. A large class of examples finds a simple and unified treatment in our approach. Applications discussed here include thermodynamical equilibrium states for Minkowski fields and quantum field theory in the Rindler's and in the open de Sitter universes. Our approach puts the above examples into perspective and unravels new possibilities for quantization. We call our generalization "extended canonical quantization" as it is suited to attack cases not directly covered by the standard canonical approach.
We study a class of three-point functions on the de Sitter universe and on the asymptotic cone. A blending of geometrical ideas and analytic methods is used to compute some remarkable integrals, on the basis of a generalized star-triangle identity living on the cone and on the complex de Sitter manifold. We discuss an application of the general results to the study of the stability of scalar particles on the Sitter universe.
We study particle decay in de Sitter space-time as given by first order perturbation theory in an interacting quantum field theory. We show that for fields with masses above a critical mass $m_c$ there is no such thing as particle stability, so that decays forbidden in flat space-time do occur there. The lifetime of such a particle also turns out to be independent of its velocity when that lifetime is comparable with de Sitter radius. Particles with lower mass are even stranger: The masses of their decay products must obey quantification rules, and their lifetime is zero.
In this paper we set up a general formalism to deal with quantum theories on a Lobatchevski space, i.e. a spatial manifold that is homogeneous, isotropic and has negative curvature. The heart of our approach is the construction of a suitable basis of plane waves which are eigenfunctions of the Laplace-Beltrami operator relative to the geometry of the curved space. These functions were previously introduced in the mathematical literature in the context of group theory; here we revisit and adapt the formalism in a way specific for quantum mechanics. Our developments render dealing with Lobatchevski spaces, which used to be quite difficult and source of controversies, easily tractable. Applications to the Milne and de Sitter universes are discussed as examples.
We study the massless minimally coupled scalar field on a two--dimensional de Sitter space-time in the setting of axiomatic quantum field theory. We construct the invariant Wightman distribution obtained as the renormalized zero--mass limit of the massive one. Insisting on gauge invariance of the model we construct a vacuum state and a Hilbert space of physical states which are invariant under the action of the whole de Sitter group. We also present the integral expression of the conserved charge which generates the gauge invariance and propose a definition of dual field.
Flat FRW perfect fluid cosmologies can be reproduced as particular solutions of suitable field theoretical models. Here we investigate the stability of perfect fluid model trajectories with respect to sets of trajectories of the corresponding field models having generic initial conditions. It is shown that the trajectories of barotropic perfect fluid models and those of the Chaplygin gas model are stable. The total probability to reach the Chaplygin gas regime early enough to achieve a matter dominated stage having a realistic duration is calculated for a scalar field model assuming a natural measure in the space of initial conditions taken near a cosmological singularity. An example is presented of a two-fluid cosmological model where the stability is partially absent.
We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary representations of the diffeomorphism group, which are important to nonrelativistic quantum statistical physics and to the quantum theory of extended objects in d-dimensional Euclidean space. Special attention is given to measurable structure and topology underlying measures on generalized configuration spaces obtained from self-similar random processes (both for d = 1 and d > 1), which describe infinite point configurations having accumulation points.
We prove a Cauchy-type integral representation for classes of functions holomorphic in four priviledged tuboid domains of the complexified one-sheeted two-dimensional hyperboloid. From a physical viewpoint, this hyperboloid can be used for describing both the two-dimensional de Sitter and anti-de Sitter universes. For two of these tuboids, called ``the Lorentz tuboids'' and relevant for de Sitter Quantum Field Theory, the boundary values onto the real hyperboloid of functions holomorphic in these domains admit continuous Fourier-Helgason-type transforms. For the other two tuboids, called the ``chiral tuboids'' and relevant for anti-de Sitter Quantum Field Theory, the boundary values on the reals of functions holomorphic in these domains admit discrete Fourier-Helgason-type transforms. In both cases, the inversion formulae for these transformations are derived by using the previous Cauchy representation for the respective classes of functions. The decomposition of functions on the real hyperboloid into sums of boundary values of holomorphic functions from the previous four tuboids gives a complete and explicit treatment of the Gelfand-Gindikin program for the one-sheeted hyperboloid.
In this note two cosmological models representing the flat Friedmann Universe filled with a Chaplygin fluid, with or without dust, are analyzed in terms of the recently proposed "statefinder" parameters. Trajectories of both models in the parameter plane are shown to be significantly different w.r.t. "quiessence" and "tracker" models. The generalized Chaplygin gas model with an equation of state of the form $p = -A/ρ^α$ is also analyzed in terms of the statefinder parameters.
We propose a general framework for studying quantum field theory on the anti-de-Sitter space-time, based on the assumption of positivity of the spectrum of the possible energy operators. In this framework we show that the n-point functions are analytic in suitable domains of the complex AdS manifold, that it is possible to Wick rotate to the Euclidean manifold and come back, and that it is meaningful to restrict AdS quantum fields to Poincare' branes. We give also a complete characterization of two-point functions which are the simplest example of our theory. Finally we prove the existence of the AdS-Unruh effect for uniformly accelerated observers on trajectories crossing the boundary of AdS at infinity, while that effect does not exist for all the other uniformly accelerated trajectories.
In this letter we show that the ``preferred'' Klein-Gordon Quantum Field Theories (QFT's) on a d-dimensional de Sitter spacetime can be obtained from a Klein-Gordon QFT on a (d+1)-dimensional ``ambient'' Minkowski spacetime satisfying the spectral condition and, conversely, that a Klein-Gordon QFT on a (d+1)-dimensional ``ambient'' Minkowski spacetime satisfying the spectral condition can be obtained as superposition of d-dimensional de Sitter Klein-Gordon fields in the preferred vacuum. These results establish a correspondence between QFT's living on manifolds having different dimensions. The method exposed here can be applied to study other situations and notably QFT on Anti de Sitter spacetime.
We propose a general framework for quantum field theory on the de Sitter space-time (i.e. for local field theories whose truncated Wightman functions are not required to vanish). By requiring that the fields satisfy a weak spectral condition, formulated in terms of the analytic continuation properties of their Wightman functions, we show that a geodesical observer will detect in the corresponding ``vacuum'' a blackbody radiation at temperature T=1/(2 πR). We also prove the analogues of the PCT, Reeh-Schlieder and Bisognano-Wichmann theorems.
We solve a continuing controversy when dealing with density fluctuations in open Friedman-Robertson-Walker universes, on the physical relevance of a class of exponential modes. We show explicitly and rigorously that these modes enter the expansion of quantum fields. In the maximally symmetric de Sitter case, encountered in inflationary models, they are excited for fields with mass below a critical value. They are seen to be responsible for the breaking of the de Sitter symmetry for a massless field. We provide an exact calculation of the power spectrum for any mass. Our method is free of the divergences that appear in earlier treatments. We extend the construction to a generic open FRW universe.