29 research outputs found
Spacelike localization of long-range fields in a model of asymptotic electrodynamics
A previously proposed algebra of asymptotic fields in quantum electrodynamics
is formulated as a net of algebras localized in regions which in general have
unbounded spacelike extension. Electromagnetic fields may be localized in
`symmetrical spacelike cones', but there are strong indications this is not
possible in the present model for charged fields, which have tails extending in
all space directions. Nevertheless, products of appropriately `dressed' fermion
fields (with compensating charges) yield bi-localized observables.Comment: 29 pages, accepted for publication in Annales Henri Poincar\'
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 Cohomological Perspective on Algebraic Quantum Field Theory
Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of constructing interacting QFT models. Symmetry is the primary tool for understanding the structure and properties of a QFT model. This perspective leads to a generalization of the algebraic quantum field theory framework, as well as a more general definition of symmetry. This means that some models may have symmetries that were not previously recognized or exploited. To first order, a deformation of a QFT model is described by a Hochschild cohomology class. A deformation could, for example, correspond to adding an interaction term to a Lagrangian. The cohomology class for such an interaction is computed here. However, the result is more general and does not require the undeformed model to be constructed from a Lagrangian. This computation leads to a more concrete version of the construction of perturbative algebraic quantum field theory
Cosmological perturbation theory and quantum gravity
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well
Batalin-Vilkovisky formalism in the functional approach to classical field theory
We develop the Batalin-Vilkovisky formalism for classical field theory on
generic globally hyperbolic spacetimes. A crucial aspect of our treatment is
the incorporation of the principle of local covariance which amounts to
formulate the theory without reference to a distinguished spacetime. In
particular, this allows a homological construction of the Poisson algebra of
observables in classical gravity. Our methods heavily rely on the differential
geometry of configuration spaces of classical fields.Comment: 42 pages, improved formulation, typos correcte
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
Properties of field functionals and characterization of local functionals
Functionals (i.e. functions of functions) are widely used in quantum field
theory and solid-state physics. In this paper, functionals are given a rigorous
mathematical framework and their main properties are described. The choice of
the proper space of test functions (smooth functions) and of the relevant
concept of differential (Bastiani differential) are discussed.
The relation between the multiple derivatives of a functional and the
corresponding distributions is described in detail. It is proved that, in a
neighborhood of every test function, the support of a smooth functional is
uniformly compactly supported and the order of the corresponding distribution
is uniformly bounded. Relying on a recent work by Yoann Dabrowski, several
spaces of functionals are furnished with a complete and nuclear topology. In
view of physical applications, it is shown that most formal manipulations can
be given a rigorous meaning.
A new concept of local functionals is proposed and two characterizations of
them are given: the first one uses the additivity (or Hammerstein) property,
the second one is a variant of Peetre's theorem. Finally, the first step of a
cohomological approach to quantum field theory is carried out by proving a
global Poincar\'e lemma and defining multi-vector fields and graded functionals
within our framework.Comment: 32 pages, no figur
The Quantum Sine-Gordon model in perturbative AQFT
We study the Sine-Gordon model with Minkowski signature in the framework of perturbative algebraic quantum field theory. We calculate the vertex operator algebra braiding property. We prove that in the finite regime of the model, the expectation value—with respect to the vacuum or a Hadamard state—of the Epstein Glaser S-matrix and the interacting current or the field respectively converge, both given as formal power series
An analogue of the Coleman-Mandula theorem for quantum field theory in curved spacetimes
The Coleman-Mandula (CM) theorem states that the Poincaré and internal symmetries of a Minkowski spacetime quantum field theory cannot combine nontrivially in an extended symmetry group. We establish an analogous result for quantum field theory in curved spacetimes, assuming local covariance, the timeslice property, a local dynamical form of Lorentz invariance, and additivity. Unlike the CM theorem, our result is valid in dimensions n≥2 and for free or interacting theories. It is formulated for theories defined on a category of all globally hyperbolic spacetimes equipped with a global coframe, on which the restricted Lorentz group acts, and makes use of a general analysis of symmetries induced by the action of a group G on the category of spacetimes. Such symmetries are shown to be canonically associated with a cohomology class in the second degree nonabelian cohomology of G with coefficients in the global gauge group of the theory. Our main result proves that the cohomology class is trivial if G is the universal cover S of the restricted Lorentz group. Among other consequences, it follows that the extended symmetry group is a direct product of the global gauge group and S, all fields transform in multiplets of S, fields of different spin do not mix under the extended group, and the occurrence of noninteger spin is controlled by the centre of the global gauge group. The general analysis is also applied to rigid scale covariance