97 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
Axiomatic quantum field theory in curved spacetime
The usual formulations of quantum field theory in Minkowski spacetime make
crucial use of features--such as Poincare invariance and the existence of a
preferred vacuum state--that are very special to Minkowski spacetime. In order
to generalize the formulation of quantum field theory to arbitrary globally
hyperbolic curved spacetimes, it is essential that the theory be formulated in
an entirely local and covariant manner, without assuming the presence of a
preferred state. We propose a new framework for quantum field theory, in which
the existence of an Operator Product Expansion (OPE) is elevated to a
fundamental status, and, in essence, all of the properties of the quantum field
theory are determined by its OPE. We provide general axioms for the OPE
coefficients of a quantum field theory. These include a local and covariance
assumption (implying that the quantum field theory is locally and covariantly
constructed from the spacetime metric), a microlocal spectrum condition, an
"associativity" condition, and the requirement that the coefficient of the
identity in the OPE of the product of a field with its adjoint have positive
scaling degree. We prove curved spacetime versions of the spin-statistics
theorem and the PCT theorem. Some potentially significant further implications
of our new viewpoint on quantum field theory are discussed.Comment: Latex, 44 pages, 2 figure
Local Thermal Equilibrium in Quantum Field Theory on Flat and Curved Spacetimes
The existence of local thermal equilibrium (LTE) states for quantum field
theory in the sense of Buchholz, Ojima and Roos is discussed in a
model-independent setting. It is shown that for spaces of finitely many
independent thermal observables there always exist states which are in LTE in
any compact region of Minkowski spacetime. Furthermore, LTE states in curved
spacetime are discussed and it is observed that the original definition of LTE
on curved backgrounds given by Buchholz and Schlemmer needs to be modified.
Under an assumption related to certain unboundedness properties of the
pointlike thermal observables, existence of states which are in LTE at a given
point in curved spacetime is established. The assumption is discussed for the
sets of thermal observables for the free scalar field considered by Schlemmer
and Verch.Comment: 16 pages, some minor changes and clarifications; section 4 has been
shortened as some unnecessary constructions have been remove
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
Conformal generally covariant quantum field theory: The scalar field and its Wick products
In this paper we generalize the construction of generally covariant quantum
theories given in the work of Brunetti, Fredenhagen and Verch to encompass the
conformal covariant case. After introducing the abstract framework, we discuss
the massless conformally coupled Klein Gordon field theory, showing that its
quantization corresponds to a functor between two certain categories. At the
abstract level, the ordinary fields, could be thought as natural
transformations in the sense of category theory. We show that, the Wick
monomials without derivatives (Wick powers), can be interpreted as fields in
this generalized sense, provided a non trivial choice of the renormalization
constants is given. A careful analysis shows that the transformation law of
Wick powers is characterized by a weight, and it turns out that the sum of
fields with different weights breaks the conformal covariance. At this point
there is a difference between the previously given picture due to the presence
of a bigger group of covariance. It is furthermore shown that the construction
does not depend upon the scale mu appearing in the Hadamard parametrix, used to
regularize the fields. Finally, we briefly discuss some further examples of
more involved fields.Comment: 21 pages, comments added, to appear on Commun. Math. Phy
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
Equivalence of the (generalised) Hadamard and microlocal spectrum condition for (generalised) free fields in curved spacetime
We prove that the singularity structure of all n-point distributions of a
state of a generalised real free scalar field in curved spacetime can be
estimated if the two-point distribution is of Hadamard form. In particular this
applies to the real free scalar field and the result has applications in
perturbative quantum field theory, showing that the class of all Hadamard
states is the state space of interest. In our proof we assume that the field is
a generalised free field, i.e. that it satisies scalar (c-number) commutation
relations, but it need not satisfy an equation of motion. The same argument
also works for anti-commutation relations and it can be generalised to
vector-valued fields. To indicate the strengths and limitations of our
assumption we also prove the analogues of a theorem by Borchers and Zimmermann
on the self-adjointness of field operators and of a very weak form of the
Jost-Schroer theorem. The original proofs of these results in the Wightman
framework make use of analytic continuation arguments. In our case no
analyticity is assumed, but to some extent the scalar commutation relations can
take its place.Comment: 18 page
Topological features of massive bosons on two dimensional Einstein space-time
In this paper we tackle the problem of constructing explicit examples of
topological cocycles of Roberts' net cohomology, as defined abstractly by
Brunetti and Ruzzi. We consider the simple case of massive bosonic quantum
field theory on the two dimensional Einstein cylinder. After deriving some
crucial results of the algebraic framework of quantization, we address the
problem of the construction of the topological cocycles. All constructed
cocycles lead to unitarily equivalent representations of the fundamental group
of the circle (seen as a diffeomorphic image of all possible Cauchy surfaces).
The construction is carried out using only Cauchy data and related net of local
algebras on the circle.Comment: 41 pages, title changed, minor changes, typos corrected, references
added. Accepted for publication in Ann. Henri Poincare
Dynamical locality of the nonminimally coupled scalar field and enlarged algebra of Wick polynomials
We discuss dynamical locality in two locally covariant quantum field
theories, the nonminimally coupled scalar field and the enlarged algebra of
Wick polynomials. We calculate the relative Cauchy evolution of the enlarged
algebra, before demonstrating that dynamical locality holds in the nonminimally
coupled scalar field theory. We also establish dynamical locality in the
enlarged algebra for the minimally coupled massive case and the conformally
coupled massive case.Comment: 39p
Covariant Counterterms and Conserved Charges in Asymptotically Flat Spacetimes
Recent work has shown that the addition of an appropriate covariant boundary
term to the gravitational action yields a well-defined variational principle
for asymptotically flat spacetimes and thus leads to a natural definition of
conserved quantities at spatial infinity. Here we connect such results to other
formalisms by showing explicitly i) that for spacetime dimension the
canonical form of the above-mentioned covariant action is precisely the ADM
action, with the familiar ADM boundary terms and ii) that for the
conserved quantities defined by counter-term methods agree precisely with the
Ashtekar-Hansen conserved charges at spatial infinity.Comment: 27 pages; Dedicated to Rafael Sorkin on the occasion of his 60th
birthday; v2 minor change
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