32 research outputs found
On the spin-statistics connection in curved spacetimes
The connection between spin and statistics is examined in the context of
locally covariant quantum field theory. A generalization is proposed in which
locally covariant theories are defined as functors from a category of framed
spacetimes to a category of -algebras. This allows for a more operational
description of theories with spin, and for the derivation of a more general
version of the spin-statistics connection in curved spacetimes than previously
available. The proof involves a "rigidity argument" that is also applied in the
standard setting of locally covariant quantum field theory to show how
properties such as Einstein causality can be transferred from Minkowski
spacetime to general curved spacetimes.Comment: 17pp. Contribution to the proceedings of the conference "Quantum
Mathematical Physics" (Regensburg, October 2014
On the spin-statistics connection in curved spacetimes
The connection between spin and statistics is examined in the context of locally covariant quantum field theory. A generalization is proposed in which locally covariant theories are defined as functors from a category of framed spacetimes to a category of ∗-algebras. This allows for a more operational description of theories with spin, and for the derivation of a more general version of the spin-statistics connection in curved spacetimes than previously available. The proof involves a "rigidity argument" that is also applied in the standard setting of locally covariant quantum field theory to show how properties such as Einstein causality can be transferred from Minkowski spacetime to general curved spacetimes
Dynamics of false vacuum bubbles: beyond the thin shell approximation
We numerically study the dynamics of false vacuum bubbles which are inside an
almost flat background; we assumed spherical symmetry and the size of the
bubble is smaller than the size of the background horizon. According to the
thin shell approximation and the null energy condition, if the bubble is
outside of a Schwarzschild black hole, unless we assume Farhi-Guth-Guven
tunneling, expanding and inflating solutions are impossible. In this paper, we
extend our method to beyond the thin shell approximation: we include the
dynamics of fields and assume that the transition layer between a true vacuum
and a false vacuum has non-zero thickness. If a shell has sufficiently low
energy, as expected from the thin shell approximation, it collapses (Type 1).
However, if the shell has sufficiently large energy, it tends to expand. Here,
via the field dynamics, field values of inside of the shell slowly roll down to
the true vacuum and hence the shell does not inflate (Type 2). If we add
sufficient exotic matters to regularize the curvature near the shell, inflation
may be possible without assuming Farhi-Guth-Guven tunneling. In this case, a
wormhole is dynamically generated around the shell (Type 3). By tuning our
simulation parameters, we could find transitions between Type 1 and Type 2, as
well as between Type 2 and Type 3. Between Type 2 and Type 3, we could find
another class of solutions (Type 4). Finally, we discuss the generation of a
bubble universe and the violation of unitarity. We conclude that the existence
of a certain combination of exotic matter fields violates unitarity.Comment: 40 pages, 41 figure
Hadamard states from null infinity
Free field theories on a four dimensional, globally hyperbolic spacetime,
whose dynamics is ruled by a Green hyperbolic partial differential operator,
can be quantized following the algebraic approach. It consists of a two-step
procedure: In the first part one identifies the observables of the underlying
physical system collecting them in a *-algebra which encodes their relational
and structural properties. In the second step one must identify a quantum
state, that is a positive, normalized linear functional on the *-algebra out of
which one recovers the interpretation proper of quantum mechanical theories via
the so-called Gelfand-Naimark-Segal theorem. In between the plethora of
possible states, only few of them are considered physically acceptable and they
are all characterized by the so-called Hadamard condition, a constraint on the
singular structure of the associated two-point function. Goal of this paper is
to outline a construction scheme for these states which can be applied whenever
the underlying background possesses a null (conformal) boundary. We discuss in
particular the examples of a real, massless conformally coupled scalar field
and of linearized gravity on a globally hyperbolic and asymptotically flat
spacetime.Comment: 23 pages, submitted to the Proceedings of the conference "Quantum
Mathematical Physics", held in Regensburg from the 29th of September to the
02nd of October 201
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
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
Dynamical locality and covariance: What makes a physical theory the same in all spacetimes?
The question of what it means for a theory to describe the same physics on
all spacetimes (SPASs) is discussed. As there may be many answers to this
question, we isolate a necessary condition, the SPASs property, that should be
satisfied by any reasonable notion of SPASs. This requires that if two theories
conform to a common notion of SPASs, with one a subtheory of the other, and are
isomorphic in some particular spacetime, then they should be isomorphic in all
globally hyperbolic spacetimes (of given dimension). The SPASs property is
formulated in a functorial setting broad enough to describe general physical
theories describing processes in spacetime, subject to very minimal
assumptions. By explicit constructions, the full class of locally covariant
theories is shown not to satisfy the SPASs property, establishing that there is
no notion of SPASs encompassing all such theories. It is also shown that all
locally covariant theories obeying the time-slice property possess two local
substructures, one kinematical (obtained directly from the functorial
structure) and the other dynamical (obtained from a natural form of dynamics,
termed relative Cauchy evolution). The covariance properties of relative Cauchy
evolution and the kinematic and dynamical substructures are analyzed in detail.
Calling local covariant theories dynamically local if their kinematical and
dynamical local substructures coincide, it is shown that the class of
dynamically local theories fulfills the SPASs property. As an application in
quantum field theory, we give a model independent proof of the impossibility of
making a covariant choice of preferred state in all spacetimes, for theories
obeying dynamical locality together with typical assumptions.Comment: 60 pages, LaTeX. Version to appear in Annales Henri Poincar
The Covariant Entropy Bound, Brane Cosmology, and the Null Energy Condition
In discussions of Bousso's Covariant Entropy Bound, the Null Energy Condition
is always assumed, as a sufficient {\em but not necessary} condition which
helps to ensure that the entropy on any lightsheet shall necessarily be finite.
The spectacular failure of the Strong Energy Condition in cosmology has,
however, led many astrophysicists and cosmologists to consider models of dark
energy which violate {\em all} of the energy conditions, and indeed the current
data do not completely rule out such models. The NEC also has a questionable
status in brane cosmology: it is probably necessary to violate the NEC in the
bulk in order to obtain a "self-tuning" theory of the cosmological constant. In
order to investigate these proposals, we modify the Karch-Randall model by
introducing NEC-violating matter into in such a way that the brane
cosmological constant relaxes to zero. The entropy on lightsheets remains
finite. However, we still find that the spacetime is fundamentally incompatible
with the Covariant Entropy Bound machinery, in the sense that it fails the
Bousso-Randall consistency condition. We argue that holography probably forbids
all {\em cosmological} violations of the NEC, and that holography is in fact
the fundamental physical principle underlying the cosmological version of the
NEC.Comment: 21 pages, 3 figures, version 2:corrected and greatly improved
discussion of the Bousso-Randall consistency check, references added;
version3: more references added, JHEP versio
Deformations of quantum field theories on spacetimes with Killing vector fields
The recent construction and analysis of deformations of quantum field
theories by warped convolutions is extended to a class of curved spacetimes.
These spacetimes carry a family of wedge-like regions which share the essential
causal properties of the Poincare transforms of the Rindler wedge in Minkowski
space. In the setting of deformed quantum field theories, they play the role of
typical localization regions of quantum fields and observables. As a concrete
example of such a procedure, the deformation of the free Dirac field is
studied.Comment: 35 pages, 3 figure
Quantum gravity from the point of view of locally covariant quantum field theory
We construct perturbative quantum gravity in a generally covariant way. In particular our construction is background independent. It is based on the locally covariant approach to quantum field theory and the renormalized Batalin-Vilkovisky formalism. We do not touch the problem of nonrenormalizability and interpret the theory as an effective theory at large length scales