1,167 research outputs found
The Hadamard Condition for Dirac Fields and Adiabatic States on Robertson-Walker Spacetimes
We characterise the homogeneous and isotropic gauge invariant and quasifree
states for free Dirac quantum fields on Robertson-Walker spacetimes in any even
dimension. Using this characterisation, we construct adiabatic vacuum states of
order corresponding to some Cauchy surface. We then show that any two such
states (of sufficiently high order) are locally quasi-equivalent. We propose a
microlocal version of the Hadamard condition for spinor fields on arbitrary
spacetimes, which is shown to entail the usual short distance behaviour of the
twopoint function. The polarisation set of these twopoint functions is
determined from the Dencker connection of the spinorial Klein-Gordon operator
which we show to equal the (pull-back) of the spin connection. Finally it is
demonstrated that adiabatic states of infinite order are Hadamard, and that
those of order correspond, in some sense, to a truncated Hadamard series
and will therefore allow for a point splitting renormalisation of the expected
stress-energy tensor.Comment: 29 pages, Latex, no figures. v2: corrections in the proof of Thm.
IV.1. v3: published versio
News vs Information
We consider the relative entropy between the vacuum state and a coherent
state in linearized quantum gravity around a stationary black hole spacetime.
Combining recent results by Casini et al. and Longo with the Raychaudhuri
equation, the following result is obtained: Let be the algebra of
observables assoiciated with a region that is the causal future of some compact
set in the interior of the spacetime. Let be the relative entropy with
respect to this algebra, the area of the horizon cross section defined by
the region, computed to second order in the gravitational perturbation. If the
region is time-translated by the Killing parameter , then , with the flux of the gravitational/matter radiation
(integrated squared news tensor) emitted towards the future of the region.Comment: 11 pages, 1 figure. arXiv admin note: text overlap with
arXiv:1903.07508, v2: some details added on function spaces and decay of
solutions, refs. adde
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
Comparison between various notions of conserved charges in asymptotically AdS-spacetimes
We derive hamiltionian generators of asymptotic symmetries for general
relativity with asymptotic AdS boundary conditions using the ``covariant phase
space'' method of Wald et al. We then compare our results with other
definitions that have been proposed in the literature. We find that our
definition agrees with that proposed by Ashtekar et al, with the spinor
definition, and with the background dependent definition of Henneaux and
Teitelboim. Our definition disagrees with the one obtained from the
``counterterm subtraction method,'' but the difference is found to consist only
of a ``constant offset'' that is determined entirely in terms of the boundary
metric. We finally discuss and justify our boundary conditions by a linear
perturbation analysis, and we comment on generalizations of our boundary
conditions, as well as inclusion of matter fields.Comment: 64p, Latex, no figures, v2: references added, typos corrected, v3:
some equations correcte
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
- …