48 research outputs found

### Anti-de Sitter space at finite temperature

We consider a conformally invariant scalar field at finite temperature in anti-de Sitter space, and find the symmetric two-point function. Since it is meromorphic and it has both a real-time and imaginary-time periodicity, it is an elliptic function. From it, the expectation values of Ăž2 and the stress-energy tensor are calculated exactly, and then compared to a Tolman-redshifted radiation gas, and to Page's âopticalâ approximation. The total energy of the radiation is finite

### BRST quantization of the massless minimally coupled scalar field in de Sitter space (zero modes, euclideanization and quantization)

We consider the massless scalar field on the four-dimensional sphere $S^4$.
Its classical action $S={1\over 2}\int_{S^4} dV (\nabla \phi)^2$ is degenerate
under the global invariance $\phi \to \phi + \hbox{constant}$. We then quantize
the massless scalar field as a gauge theory by constructing a BRST-invariant
quantum action. The corresponding gauge-breaking term is a non-local one of the
form $S^{\rm GB}={1\over {2\alpha V}}\bigl(\int_{S^4} dV \phi \bigr)^2$ where
$\alpha$ is a gauge parameter and $V$ is the volume of $S^4$. It allows us to
correctly treat the zero mode problem. The quantum theory is invariant under
SO(5), the symmetry group of $S^4$, and the associated two-point functions have
no infrared divergence. The well-known infrared divergence which appears by
taking the massless limit of the massive scalar field propagator is therefore a
gauge artifact. By contrast, the massless scalar field theory on de Sitter
space $dS^4$ - the lorentzian version of $S^4$ - is not invariant under the
symmetry group of that spacetime SO(1,4). Here, the infrared divergence is
real. Therefore, the massless scalar quantum field theories on $S^4$ and $dS^4$
cannot be linked by analytic continuation. In this case, because of zero modes,
the euclidean approach to quantum field theory does not work. Similar
considerations also apply to massive scalar field theories for exceptional
values of the mass parameter (corresponding to the discrete series of the de
Sitter group).Comment: This paper has been published under the title "Zero modes,
euclideanization and quantization" [Phys. Rev. D46, 2553 (1992)

### Green's function for the Hodge Laplacian on some classes of Riemannian and Lorentzian symmetric spaces

We compute the Green's function for the Hodge Laplacian on the symmetric
spaces M\times\Sigma, where M is a simply connected n-dimensional Riemannian or
Lorentzian manifold of constant curvature and \Sigma is a simply connected
Riemannian surface of constant curvature. Our approach is based on a
generalization to the case of differential forms of the method of spherical
means and on the use of Riesz distributions on manifolds. The radial part of
the Green's function is governed by a fourth order analogue of the Heun
equation.Comment: 18 page

### Fractional S-branes on a Spacetime Orbifold

Unstable D-branes are central objects in string theory, and exist also in
time-dependent backgrounds. In this paper we take first steps to studying brane
decay in spacetime orbifolds. As a concrete model we focus on the R^{1,d}/Z_2
orbifold. We point out that on a spacetime orbifold there exist two kinds of
S-branes, fractional S-branes in addition to the usual ones. We investigate
their construction in the open string and closed string boundary state
approach. As an application of these constructions, we consider a scenario
where an unstable brane nucleates at the origin of time of a spacetime, its
initial energy then converting into energy flux in the form of closed strings.
The dual open string description allows for a well-defined description of this
process even if it originates at a singular origin of the spacetime.Comment: 22 pages, 6 eps figure

### Massless scalar fields and infrared divergences in the inflationary brane world

We study the quantum effects induced by bulk scalar fields in a model with a
de Sitter (dS) brane in a flat bulk (the Vilenkin-Ipser-Sikivie model) in more
than four dimensions. In ordinary dS space, it is well known that the stress
tensor in the dS invariant vacuum for an effectively massless scalar
(m_\eff^2=m^2+\xi {\cal R}=0 with ${\cal R}$ the Ricci scalar) is infrared
divergent except for the minimally coupled case. The usual procedure to tame
this divergence is to replace the dS invariant vacuum by the Allen Follaci (AF)
vacuum. The resulting stress tensor breaks dS symmetry but is regular.
Similarly, in the brane world context, we find that the dS invariant vacuum
generates \tmn divergent everywhere when the lowest lying mode becomes
massless except for massless minimal coupling case. A simple extension of the
AF vacuum to the present case avoids this global divergence, but \tmn remains
to be divergent along a timelike axis in the bulk. In this case, singularities
also appear along the light cone emanating from the origin in the bulk,
although they are so mild that \tmn stays finite except for non-minimal
coupling cases in four or six dimensions. We discuss implications of these
results for bulk inflaton models. We also study the evolution of the field
perturbations in dS brane world. We find that perturbations grow linearly with
time on the brane, as in the case of ordinary dS space. In the bulk, they are
asymptotically bounded.Comment: 20 pages. References adde

### Massless Minimally Coupled Fields in De Sitter Space: O(4)-Symmetric States Versus De Sitter Invariant Vacuum

The issue of de Sitter invariance for a massless minimally coupled scalar
field is revisited. Formally, it is possible to construct a de Sitter invariant
state for this case provided that the zero mode of the field is quantized
properly. Here we take the point of view that this state is physically
acceptable, in the sense that physical observables can be computed and have a
reasonable interpretation. In particular, we use this vacuum to derive a new
result: that the squared difference between the field at two points along a
geodesic observer's space-time path grows linearly with the observer's proper
time for a quantum state that does not break de Sitter invariance. Also, we use
the Hadamard formalism to compute the renormalized expectation value of the
energy momentum tensor, both in the O(4) invariant states introduced by Allen
and Follaci, and in the de Sitter invariant vacuum. We find that the vacuum
energy density in the O(4) invariant case is larger than in the de Sitter
invariant case.Comment: TUTP-92-1, to appear in Phys. Rev.

### Analytical approximation of the stress-energy tensor of a quantized scalar field in static spherically symmetric spacetimes

Analytical approximations for ${}$ and ${}$ of a
quantized scalar field in static spherically symmetric spacetimes are obtained.
The field is assumed to be both massive and massless, with an arbitrary
coupling $\xi$ to the scalar curvature, and in a zero temperature vacuum state.
The expressions for ${}$ and ${}$ are divided into
low- and high-frequency parts. The contributions of the high-frequency modes to
these quantities are calculated for an arbitrary quantum state. As an example,
the low-frequency contributions to ${}$ and ${}$ are
calculated in asymptotically flat spacetimes in a quantum state corresponding
to the Minkowski vacuum (Boulware quantum state). The limits of the
applicability of these approximations are discussed.Comment: revtex4, 17 pages; v2: three references adde

### The averaged null energy condition for general quantum field theories in two dimensions

It is shown that the averaged null energy condition is fulfilled for a dense,
translationally invariant set of vector states in any local quantum field
theory in two-dimensional Minkowski spacetime whenever the theory has a mass
gap and possesses an energy-momentum tensor. The latter is assumed to be a
Wightman field which is local relative to the observables, generates locally
the translations, is divergence-free, and energetically bounded. Thus the
averaged null energy condition can be deduced from completely generic, standard
assumptions for general quantum field theory in two-dimensional flat spacetime.Comment: LateX2e, 16 pages, 1 eps figur

### The averaged null energy condition and difference inequalities in quantum field theory

Recently, Larry Ford and Tom Roman have discovered that in a flat cylindrical
space, although the stress-energy tensor itself fails to satisfy the averaged
null energy condition (ANEC) along the (non-achronal) null geodesics, when the
``Casimir-vacuum" contribution is subtracted from the stress-energy the
resulting tensor does satisfy the ANEC inequality. Ford and Roman name this
class of constraints on the quantum stress-energy tensor ``difference
inequalities." Here I give a proof of the difference inequality for a minimally
coupled massless scalar field in an arbitrary two-dimensional spacetime, using
the same techniques as those we relied on to prove ANEC in an earlier paper
with Robert Wald. I begin with an overview of averaged energy conditions in
quantum field theory.Comment: 20 page

### Spatiotemporal complexity of the universe at subhorizon scales

This is a short note on the spatiotemporal complexity of the dynamical
state(s) of the universe at subhorizon scales (up to 300 Mpc). There are
reasons, based mainly on infrared radiative divergences, to believe that one
can encounter a flicker noise in the time domain, while in the space domain,
the scaling laws are reflected in the (multi)fractal distribution of galaxies
and their clusters. There exist recent suggestions on a unifying treatment of
these two aspects within the concept of spatiotemporal complexity of dynamical
systems driven out of equilibrium. Spatiotemporal complexity of the subhorizon
dynamical state(s) of the universe is a conceptually nice idea and may lead to
progress in our understanding of the material structures at large scalesComment: references update