101 research outputs found
Holgraphy and BMS field theory
We study the key ingredients of a candidate holographic correspondence in an
asymptotically flat spacetimes; in particular we develop the kinematical and
the classical dynamical data of a BMS invariant field theory living at null
infinity.Comment: 3 pages, to appear in the Proceedings for the ``XVI SIGRAV
Conference'' in Vietri sul Mare (SA) 13-16 Septembe
Curvature fluctuations on asymptotically de Sitter spacetimes via the semiclassical Einstein's equations
It has been proposed recently to consider in the framework of cosmology an
extension of the semiclassical Einstein's equations in which the Einstein
tensor is considered as a random function. This paradigm yields a hierarchy of
equations between the -point functions of the quantum, normal ordered,
stress energy-tensor and those associated to the stochastic Einstein tensor.
Assuming that the matter content is a conformally coupled massive scalar field
on de Sitter spacetime, this framework has been applied to compute the power
spectrum of the quantum fluctuations and to show that it is almost
scale-invariant. We test the robustness and the range of applicability of this
proposal by applying it to a less idealized, but physically motivated,
scenario, namely we consider Friedmann-Robertson-Walker spacetimes which behave
only asymptotically in the past as a de Sitter spacetime. We show in particular
that, under this new assumption and independently from any renormalization
freedom, the power spectrum associated to scalar perturbations of the metric
behaves consistently with an almost scale-invariant power spectrum.Comment: 23 page
Models of free quantum field theories on curved backgrounds
Free quantum field theories on curved backgrounds are discussed via three
explicit examples: the real scalar field, the Dirac field and the Proca field.
The first step consists of outlining the main properties of globally hyperbolic
spacetimes, that is the class of manifolds on which the classical dynamics of
all physically relevant free fields can be written in terms of a Cauchy
problem. The set of all smooth solutions of the latter encompasses the
dynamically allowed configurations which are used to identify via a suitable
pairing a collection of classical observables. As a last step we use such
collection to construct a -algebra which encodes the information on the
dynamics and on the canonical commutation or anti-commutation relations
depending whether the underlying field is a Fermion or a Boson.Comment: 41 page
IDEAL characterization of isometry classes of FLRW and inflationary spacetimes
In general relativity, an IDEAL (Intrinsic, Deductive, Explicit, ALgorithmic)
characterization of a reference spacetime metric consists of a set of
tensorial equations , constructed covariantly out of the metric ,
its Riemann curvature and their derivatives, that are satisfied if and only if
is locally isometric to the reference spacetime metric . The same
notion can be extended to also include scalar or tensor fields, where the
equations are allowed to also depend on the extra fields .
We give the first IDEAL characterization of cosmological FLRW spacetimes, with
and without a dynamical scalar (inflaton) field. We restrict our attention to
what we call regular geometries, which uniformly satisfy certain identities or
inequalities. They roughly split into the following natural special cases:
constant curvature spacetime, Einstein static universe, and flat or curved
spatial slices. We also briefly comment on how the solution of this problem has
implications, in general relativity and inflation theory, for the construction
of local gauge invariant observables for linear cosmological perturbations and
for stability analysis.Comment: v4: Fixed minor typos relative to published version. v3: 42 pages;
restructured order of sections, fixed some inconsistent formulas; close to
published versio
Electromagnetism, local covariance, the Aharonov-Bohm effect and Gauss' law
We quantise the massless vector potential A of electromagnetism in the
presence of a classical electromagnetic (background) current, j, in a generally
covariant way on arbitrary globally hyperbolic spacetimes M. By carefully
following general principles and procedures we clarify a number of topological
issues. First we combine the interpretation of A as a connection on a principal
U(1)-bundle with the perspective of general covariance to deduce a physical
gauge equivalence relation, which is intimately related to the Aharonov-Bohm
effect. By Peierls' method we subsequently find a Poisson bracket on the space
of local, affine observables of the theory. This Poisson bracket is in general
degenerate, leading to a quantum theory with non-local behaviour. We show that
this non-local behaviour can be fully explained in terms of Gauss' law. Thus
our analysis establishes a relationship, via the Poisson bracket, between the
Aharonov-Bohm effect and Gauss' law (a relationship which seems to have gone
unnoticed so far). Furthermore, we find a formula for the space of electric
monopole charges in terms of the topology of the underlying spacetime. Because
it costs little extra effort, we emphasise the cohomological perspective and
derive our results for general p-form fields A (p < dim(M)), modulo exact
fields. In conclusion we note that the theory is not locally covariant, in the
sense of Brunetti-Fredenhagen-Verch. It is not possible to obtain such a theory
by dividing out the centre of the algebras, nor is it physically desirable to
do so. Instead we argue that electromagnetism forces us to weaken the axioms of
the framework of local covariance, because the failure of locality is
physically well-understood and should be accommodated.Comment: Minor corrections to Def. 4.3, acknowledgements and typos, in line
with published versio
Quantum field theory on affine bundles
We develop a general framework for the quantization of bosonic and fermionic
field theories on affine bundles over arbitrary globally hyperbolic spacetimes.
All concepts and results are formulated using the language of category theory,
which allows us to prove that these models satisfy the principle of general
local covariance. Our analysis is a preparatory step towards a full-fledged
quantization scheme for the Maxwell field, which emphasises the affine bundle
structure of the bundle of principal U(1)-connections. As a by-product, our
construction provides a new class of exactly tractable locally covariant
quantum field theories, which are a mild generalization of the linear ones. We
also show the existence of a functorial assignment of linear quantum field
theories to affine ones. The identification of suitable algebra homomorphisms
enables us to induce whole families of physical states (satisfying the
microlocal spectrum condition) for affine quantum field theories by pulling
back quasi-free Hadamard states of the underlying linear theories.Comment: 34 pages, no figures; v2: 35 pages, compatible with version to be
published in Annales Henri Poincar
The Casimir effect from the point of view of algebraic quantum field theory
We consider a region of Minkowski spacetime bounded either by one or by two
parallel, infinitely extended plates orthogonal to a spatial direction and a
real Klein-Gordon field satisfying Dirichlet boundary conditions. We quantize
these two systems within the algebraic approach to quantum field theory using
the so-called functional formalism. As a first step we construct a suitable
unital *-algebra of observables whose generating functionals are characterized
by a labelling space which is at the same time optimal and separating and
fulfils the F-locality property. Subsequently we give a definition for these
systems of Hadamard states and we investigate explicit examples. In the case of
a single plate, it turns out that one can build algebraic states via a
pull-back of those on the whole Minkowski spacetime, moreover inheriting from
them the Hadamard property. When we consider instead two plates, algebraic
states can be put in correspondence with those on flat spacetime via the
so-called method of images, which we translate to the algebraic setting. For a
massless scalar field we show that this procedure works perfectly for a large
class of quasi-free states including the Poincar\'e vacuum and KMS states.
Eventually Wick polynomials are introduced. Contrary to the Minkowski case, the
extended algebras, built in globally hyperbolic subregions can be collected in
a global counterpart only after a suitable deformation which is expressed
locally in terms of a *-isomorphism. As a last step, we construct explicitly
the two-point function and the regularized energy density, showing, moreover,
that the outcome is consistent with the standard results of the Casimir effect.Comment: 45 pages, section 2 improved, typos correcte
Hadamard States From Light-like Hypersurfaces
This book provides a rather self-contained survey of the construction of
Hadamard states for scalar field theories in a large class of notable
spacetimes, possessing a (conformal) light-like boundary. The first two
sections focus on explaining a few introductory aspects of this topic and on
providing the relevant geometric background material. The notions of
asymptotically flat spacetimes and of expanding universes with a cosmological
horizon are analysed in detail, devoting special attention to the
characterization of asymptotic symmetries. In the central part of the book, the
quantization of a real scalar field theory on such class of backgrounds is
discussed within the framework of algebraic quantum field theory. Subsequently
it is explained how it is possible to encode the information of the observables
of the theory in a second, ancillary counterpart, which is built directly on
the conformal (null) boundary. This procedure, dubbed bulk-to-boundary
correspondence, has the net advantage of allowing the identification of a
distinguished state for the theory on the boundary, which admits a counterpart
in the bulk spacetime which is automatically of Hadamard form. In the last part
of the book, some applications of these states are discussed, in particular the
construction of the algebra of Wick polynomials. This book is aimed mainly, but
not exclusively, at a readership with interest in the mathematical formulation
of quantum field theory on curved backgrounds.Comment: 106 pages, 2 figures, to appear in SpringerBriefs in Mathematical
Physics, references adde
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