1,128 research outputs found
Quantum field theory in curved spacetime, the operator product expansion, and dark energy
To make sense of quantum field theory in an arbitrary (globally hyperbolic)
curved spacetime, the theory must be formulated in a local and covariant manner
in terms of locally measureable field observables. Since a generic curved
spacetime does not possess symmetries or a unique notion of a vacuum state, the
theory also must be formulated in a manner that does not require symmetries or
a preferred notion of a ``vacuum state'' and ``particles''. We propose such a
formulation of quantum field theory, wherein the operator product expansion
(OPE) of the quantum fields is elevated to a fundamental status, and the
quantum field theory is viewed as being defined by its OPE. Since the OPE
coefficients may be better behaved than any quantities having to do with
states, we suggest that it may be possible to perturbatively construct the OPE
coefficients--and, thus, the quantum field theory. By contrast, ground/vacuum
states--in spacetimes, such as Minkowski spacetime, where they may be
defined--cannot vary analytically with the parameters of the theory. We argue
that this implies that composite fields may acquire nonvanishing vacuum state
expectation values due to nonperturbative effects. We speculate that this could
account for the existence of a nonvanishing vacuum expectation value of the
stress-energy tensor of a quantum field occurring at a scale much smaller than
the natural scales of the theory.Comment: 9 pages, essay awarded 4th prize by Gravity Research Foundatio
Conservation of the stress tensor in perturbative interacting quantum field theory in curved spacetimes
We propose additional conditions (beyond those considered in our previous
papers) that should be imposed on Wick products and time-ordered products of a
free quantum scalar field in curved spacetime. These conditions arise from a
simple ``Principle of Perturbative Agreement'': For interaction Lagrangians
that are such that the interacting field theory can be constructed
exactly--as occurs when is a ``pure divergence'' or when is at most
quadratic in the field and contains no more than two derivatives--then
time-ordered products must be defined so that the perturbative solution for
interacting fields obtained from the Bogoliubov formula agrees with the exact
solution. The conditions derived from this principle include a version of the
Leibniz rule (or ``action Ward identity'') and a condition on time-ordered
products that contain a factor of the free field or the free
stress-energy tensor . The main results of our paper are (1) a proof
that in spacetime dimensions greater than 2, our new conditions can be
consistently imposed in addition to our previously considered conditions and
(2) a proof that, if they are imposed, then for {\em any} polynomial
interaction Lagrangian (with no restriction on the number of derivatives
appearing in ), the stress-energy tensor of the interacting
theory will be conserved. Our work thereby establishes (in the context of
perturbation theory) the conservation of stress-energy for an arbitrary
interacting scalar field in curved spacetimes of dimension greater than 2. Our
approach requires us to view time-ordered products as maps taking classical
field expressions into the quantum field algebra rather than as maps taking
Wick polynomials of the quantum field into the quantum field algebra.Comment: 88 pages, latex, no figures, v2: changes in the proof of proposition
3.
Further restrictions on the topology of stationary black holes in five dimensions
We place further restriction on the possible topology of stationary
asymptotically flat vacuum black holes in 5 spacetime dimensions. We prove that
the horizon manifold can be either a connected sum of Lens spaces and "handles"
, or the quotient of by certain finite groups of
isometries (with no "handles"). The resulting horizon topologies include Prism
manifolds and quotients of the Poincare homology sphere. We also show that the
topology of the domain of outer communication is a cartesian product of the
time direction with a finite connected sum of 's
and 's, minus the black hole itself. We do not assume the existence of
any Killing vector beside the asymptotically timelike one required by
definition for stationarity.Comment: LaTex, 22 pages, 9 figure
Supersymmetric Field-Theoretic Models on a Supermanifold
We propose the extension of some structural aspects that have successfully
been applied in the development of the theory of quantum fields propagating on
a general spacetime manifold so as to include superfield models on a
supermanifold. We only deal with the limited class of supermanifolds which
admit the existence of a smooth body manifold structure. Our considerations are
based on the Catenacci-Reina-Teofillatto-Bryant approach to supermanifolds. In
particular, we show that the class of supermanifolds constructed by
Bonora-Pasti-Tonin satisfies the criterions which guarantee that a
supermanifold admits a Hausdorff body manifold. This construction is the
closest to the physicist's intuitive view of superspace as a manifold with some
anticommuting coordinates, where the odd sector is topologically trivial. The
paper also contains a new construction of superdistributions and useful results
on the wavefront set of such objects. Moreover, a generalization of the
spectral condition is formulated using the notion of the wavefront set of
superdistributions, which is equivalent to the requirement that all of the
component fields satisfy, on the body manifold, a microlocal spectral condition
proposed by Brunetti-Fredenhagen-K\"ohler.Comment: Final version to appear in J.Math.Phy
Perturbative Construction of Models of Algebraic Quantum Field Theory
We review the construction of models of algebraic quantum field theory by
renormalized perturbation theory.Comment: 38 page
On leading order gravitational backreactions in de Sitter spacetime
Backreactions are considered in a de Sitter spacetime whose cosmological
constant is generated by the potential of scalar field. The leading order
gravitational effect of nonlinear matter fluctuations is analyzed and it is
found that the initial value problem for the perturbed Einstein equations
possesses linearization instabilities. We show that these linearization
instabilities can be avoided by assuming strict de Sitter invariance of the
quantum states of the linearized fluctuations. We furthermore show that quantum
anomalies do not block the invariance requirement. This invariance constraint
applies to the entire spectrum of states, from the vacuum to the excited states
(should they exist), and is in that sense much stronger than the usual Poincare
invariance requirement of the Minkowski vacuum alone. Thus to leading order in
their effect on the gravitational field, the quantum states of the matter and
metric fluctuations must be de Sitter invariant.Comment: 12 pages, no figures, typos corrected and some clarifying comments
added, version accepted by Phys. Rev.
Stability in Designer Gravity
We study the stability of designer gravity theories, in which one considers
gravity coupled to a tachyonic scalar with anti-de Sitter boundary conditions
defined by a smooth function W. We construct Hamiltonian generators of the
asymptotic symmetries using the covariant phase space method of Wald et al.and
find they differ from the spinor charges except when W=0. The positivity of the
spinor charge is used to establish a lower bound on the conserved energy of any
solution that satisfies boundary conditions for which has a global minimum.
A large class of designer gravity theories therefore have a stable ground
state, which the AdS/CFT correspondence indicates should be the lowest energy
soliton. We make progress towards proving this, by showing that minimum energy
solutions are static. The generalization of our results to designer gravity
theories in higher dimensions involving several tachyonic scalars is discussed.Comment: 29 page
Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory
On the basis of a thorough discussion of the Batalin-Vilkovisky formalism for
classical field theory presented in our previous publication, we construct in
this paper the Batalin-Vilkovisky complex in perturbatively renormalized
quantum field theory. The crucial technical ingredient is a proof that the
renormalized time-ordered product is equivalent to the pointwise product of
classical field theory. The renormalized Batalin-Vilkovisky algebra is then the
classical algebra but written in terms of the time-ordered product, together
with an operator which replaces the ill defined graded Laplacian of the
unrenormalized theory. We identify it with the anomaly term of the anomalous
Master Ward Identity of Brennecke and D\"utsch. Contrary to other approaches we
do not refer to the path integral formalism and do not need to use
regularizations in intermediate steps.Comment: 34 page
A remark on alpha vacua for quantum field theories on de Sitter space
It is shown that the so-called -vacua which have been proposed as
candidates for states of free quantum fields on de Sitter space have infinitely
strong fluctuations for typical observables as averaged renormalized energy
momentum tensor
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