482 research outputs found
Global Existence of Solutions of the Semiclassical Einstein Equation for Cosmological Spacetimes
We study the solutions of the semiclassical Einstein equation in flat
cosmological spacetimes driven by a massive conformally coupled scalar field.
In particular, we show that it is possible to give initial conditions at finite
time to get a state for the quantum field which gives finite expectation values
for the stress-energy tensor. Furthermore, it is possible to control this
expectation value by means of a global estimate on regular cosmological
spacetimes. The obtained estimates permit to write a theorem about the
existence and uniqueness of the local solutions encompassing both the spacetime
metric and the matter field simultaneously. Finally, we show that one can
always extend local solutions up to a point where the scale factor becomes
singular or the Hubble function reaches a critical value ,
which both correspond to a divergence of the scalar curvature, namely a
spacetime singularity.Comment: 20 pages; corrected reference
Electromagnetic Potential in Pre-Metric Electrodynamics: Causal Structure, Propagators and Quantization
An axiomatic approach to electrodynamics reveals that Maxwell electrodynamics
is just one instance of a variety of theories for which the name
electrodynamics is justified. They all have in common that their fundamental
input are Maxwell's equations (or ) and
and a constitutive law H = # F which relates the field
strength two-form and the excitation two-form . A local and linear
constitutive law defines what is called local and linear pre-metric
electrodynamics whose best known application are the effective description of
electrodynamics inside media including, e.g., birefringence. We analyze the
classical theory of the electromagnetic potential before we use methods
familiar from mathematical quantum field theory in curved spacetimes to
quantize it in a locally covariant way. Our analysis of the classical theory
contains the derivation of retarded and advanced propagators, the analysis of
the causal structure on the basis of the constitutive law (instead of a metric)
and a discussion of the classical phase space. This classical analysis sets the
stage for the construction of the quantum field algebra and quantum states.
Here one sees, among other things, that a microlocal spectrum condition can be
formulated in this more general setting.Comment: 34 pages, references added, update to published version, title
updated to published versio
An Evolution Equation Approach to Linear Quantum Field Theory
In the first part of our paper we analyze bisolutions and inverses of
(non-autonomous) evolution equations. We are mostly interested in
pseudo-unitary evolutions on Krein spaces, which naturally arise in linear
Quantum Field Theory. We prove that with boundary conditions given by a maximal
positive and maximal negative space we can associate an inverse, which can be
viewed as a generalization of the usual Feynman propagator. In the context of
globally hyperbolic manifolds, the Feynman propagator turns out to be a
distinguished inverse of the Klein-Gordon operator. Within the formalism of
Quantum Field Theory on curved spacetimes, the Feynman propagator yields the
expectation values of time-ordered products of fields between the in and out
vacuum --the basic ingredient for Feynman diagrams.Comment: 61 page
Hadamard States for the Vector Potential on Asymptotically Flat Spacetimes
We develop a quantization scheme for the vector potential on globally
hyperbolic spacetimes which realizes it as a locally covariant conformal
quantum field theory. This result allows us to employ on a large class of
backgrounds, which are asymptotically flat at null infinity, a bulk-to-boundary
correspondence procedure in order to identify for the underlying field algebra
a distinguished ground state which is of Hadamard form.Comment: 25 pages, comments added, improved notation, minor typos corrected
and updated bibliograph
Scale-Invariant Curvature Fluctuations from an Extended Semiclassical Gravity
We present an extension of the semiclassical Einstein equations which couples
n-point correlation functions of a stochastic Einstein tensor to the n-point
functions of the quantum stress-energy tensor. We apply this extension to
calculate the quantum fluctuations during an inflationary period, where we take
as a model a massive conformally coupled scalar field on a perturbed de Sitter
space and describe how a renormalization independent, almost-scale-invariant
power spectrum of the scalar metric perturbation is produced. Furthermore, we
discuss how this model yields a natural basis for the calculation of
non-Gaussianities of the considered metric fluctuations.Comment: 16 pages, 2 figures; final versio
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