Results 1  10
of
689
Microlocal analysis and interacting quantum field theory: Renormalizability on Physical Backgrounds
, 1999
"... We present a perturbative construction of interacting quantum field theories on smooth globally hyperbolic (curved) spacetimes. We develop a purely local version of the StückelbergBogoliubovEpsteinGlaser method of renormalization by using techniques from microlocal analysis. Relying on recent r ..."
Abstract

Cited by 163 (22 self)
 Add to MetaCart
(Show Context)
We present a perturbative construction of interacting quantum field theories on smooth globally hyperbolic (curved) spacetimes. We develop a purely local version of the StückelbergBogoliubovEpsteinGlaser method of renormalization by using techniques from microlocal analysis. Relying on recent results of Radzikowski, Köhler and the authors about a formulation of a local spectrum condition in terms of wave front sets of correlation functions of quantum fields on curved spacetimes, we construct timeordered operatorvalued products of Wick polynomials of free fields. They serve as building blocks for a local (perturbative) definition of interacting fields. Renormalization in this framework amounts to extensions of expectation values of timeordered products to all points of spacetime. The extensions are classified according to a microlocal generalization of Steinmann scaling degree corresponding to the degree of divergence in other renormalization schemes. As a result, we prove that the usual perturbative classification of interacting quantum
The generally covariant locality principle  A new paradigm for local quantum physics
 COMMUN.MATH.PHYS
, 2001
"... A new approach to the modelindependent description of quantum field theories will be introduced in the present work. The main feature of this new approach is to incorporate in a local sense the principle of general covariance of general relativity, thus giving rise to the concept of a locally cova ..."
Abstract

Cited by 147 (21 self)
 Add to MetaCart
(Show Context)
A new approach to the modelindependent description of quantum field theories will be introduced in the present work. The main feature of this new approach is to incorporate in a local sense the principle of general covariance of general relativity, thus giving rise to the concept of a locally covariant quantum field theory. Such locally covariant quantum field theories will be described mathematically in terms of covariant functors between the categories, on one side, of globally hyperbolic spacetimes with isometric embeddings as morphisms and, on the other side, of ∗algebras with unital injective ∗endomorphisms as morphisms. Moreover, locally covariant quantum fields can be described in this framework as natural transformations between certain functors. The usual HaagKastler framework of nets of operatoralgebras over a fixed spacetime backgroundmanifold, together with covariant automorphic actions of the isometrygroup of the background spacetime, can be regained from this new approach as a special case. Examples of this new approach are also outlined. In case that a locally covariant quantum field theory obeys the
The holographic principle
 Rev. Mod. Phys
, 2002
"... There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at 1.4 ×10 69 bits per square meter. We review the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black hole ..."
Abstract

Cited by 125 (7 self)
 Add to MetaCart
(Show Context)
There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at 1.4 ×10 69 bits per square meter. We review the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of lightsheets, which associate relevant spacetime regions to any
Local Wick Polynomials and Time Ordered Products of Quantum Fields in Curved Spacetime
, 2008
"... In order to have well defined rules for the perturbative calculation of quantities of interest in an interacting quantum field theory in curved spacetime, it is necessary to construct Wick polynomials and their time ordered products for the noninteracting theory. A construction of these quantities h ..."
Abstract

Cited by 111 (10 self)
 Add to MetaCart
In order to have well defined rules for the perturbative calculation of quantities of interest in an interacting quantum field theory in curved spacetime, it is necessary to construct Wick polynomials and their time ordered products for the noninteracting theory. A construction of these quantities has recently been given by Brunetti, Fredenhagen, and Köhler, and by Brunetti and Fredenhagen, but they did not impose any “locality ” or “covariance ” condition in their constructions. As a consequence, their construction of time ordered products contained ambiguities involving arbitrary functions of spacetime point rather than arbitrary parameters. In this paper, we construct an “extended Wick polynomial algebra”—large enough to contain the Wick polynomials and their time ordered products—by generalizing a construction of Dütsch and Fredenhagen to curved spacetime. We then define the notion of a local, covariant quantum field, and seek a definition of local Wick polynomials and their time ordered products as local, covariant quantum fields. We introduce a new notion of the scaling behavior of a local, covariant quantum field, and impose scaling requirements on our local Wick polynomials and their time ordered products as well as certain additional requirements—such as commutation relations with the free field and appropriate continuity properties under variations of the spacetime metric. For a given polynomial order in powers of the field, we prove that these conditions uniquely determine the local Wick polynomials and their time ordered products up to a finite number of parameters. (These parameters correspond to the usual renormalization ambiguities occurring in Minkowski spacetime together with
The Thermodynamics of Black Holes
, 2000
"... We review the present status of black hole thermodynamics. Our review includes discussion of classical black hole thermodynamics, Hawking radiation from black holes, the generalized second law, and the issue of entropy bounds. A brief survey also is given of approaches to the calculation of black ho ..."
Abstract

Cited by 105 (1 self)
 Add to MetaCart
(Show Context)
We review the present status of black hole thermodynamics. Our review includes discussion of classical black hole thermodynamics, Hawking radiation from black holes, the generalized second law, and the issue of entropy bounds. A brief survey also is given of approaches to the calculation of black hole entropy. We conclude with a discussion of some unresolved open issues.
On the rigidity theorem for spacetimes with a stationary event horizon or a compact Cauchy horizon
"... We consider smooth electrovac spacetimes which represent either (A) an asymptotically flat, stationary black hole or (B) a cosmological spacetime with a compact Cauchy horizon ruled by closed null geodesics. The black hole event horizon or, respectively, the compact Cauchy horizon of these spacetime ..."
Abstract

Cited by 71 (8 self)
 Add to MetaCart
(Show Context)
We consider smooth electrovac spacetimes which represent either (A) an asymptotically flat, stationary black hole or (B) a cosmological spacetime with a compact Cauchy horizon ruled by closed null geodesics. The black hole event horizon or, respectively, the compact Cauchy horizon of these spacetimes is assumed to be a smooth null hypersurface which is nondegenerate in the sense that its null geodesic generators are geodesically incomplete in one direction. In both cases, it is shown that there exists a Killing vector field in a onesided neighborhood of the horizon which is normal to the horizon. We thereby generalize theorems of Hawking (for case (A)) and Isenberg and Moncrief (for case (B)) to the nonanalytic case. 1
Microlocal spectrum condition and Hadamard form . . .
, 2000
"... The characterization of Hadamard states in terms of a specific form of the wavefront set of their twopoint functions has been developed some years ago by Radzikowski for scalar fields on a fourdimensional globally hyperbolic spacetime, and initiated a major progress in the understanding of Hadam ..."
Abstract

Cited by 48 (4 self)
 Add to MetaCart
The characterization of Hadamard states in terms of a specific form of the wavefront set of their twopoint functions has been developed some years ago by Radzikowski for scalar fields on a fourdimensional globally hyperbolic spacetime, and initiated a major progress in the understanding of Hadamard states and the further development of quantum field theory in curved spacetime. In the present work, the characterization of Hadamard states through a particular form of the wavefront set of their twopoint functions will be generalized from scalar fields to vector fields (sections in a vector bundle) which are subject to a waveequation and are quantized so as to fulfill the covariant canonical commutation relations, or which obey a Dirac equation and are quantized according to the covariant anticommutation relations, in any globally hyperbolic spacetime having dimension three or higher. In proving this result, a gap which is present in the published proof for the scalar field case will be removed. Moreover we determine the shortdistance scaling limits of Hadamard states for vectorbundle valued fields, finding them to coincide with the corresponding flatspace, massless vacuum states.
Thermodynamics of (3+1)dimensional black holes with toroidal or higher genus black horizons, Phys. Rev. D56
, 1997
"... grqc/9705012 ..."
(Show Context)
Wave equations on Lorentzian manifolds and quantization
, 2007
"... In General Relativity spacetime is described mathematically by a Lorentzian manifold. Gravitation manifests itself as the curvature of this manifold. Physical fields, such as the electromagnetic field, are defined on this manifold and have to satisfy a wave equation. This book provides an introducti ..."
Abstract

Cited by 45 (0 self)
 Add to MetaCart
(Show Context)
In General Relativity spacetime is described mathematically by a Lorentzian manifold. Gravitation manifests itself as the curvature of this manifold. Physical fields, such as the electromagnetic field, are defined on this manifold and have to satisfy a wave equation. This book provides an introduction to the theory of linear wave equations on Lorentzian manifolds. In contrast to other texts on this topic [Friedlander1975, Günther1988] we develop the global theory. This means, we ask for existence and uniqueness of solutions which are defined on all of the underlying manifold. Such results are of great importance and are already used much in the literature despite the fact that published proofs are missing. Tracing back the references one typically ends at Leray’s unpublished lecture notes [Leray1953] or their exposition [ChoquetBruhat1968]. In this text we develop the global theory from scratch in a modern geometric language. In the first chapter we provide basic definitions and facts about distributions on manifolds, Lorentzian geometry, and normally hyperbolic operators. We study the building blocks for local solutions, the Riesz distributions, in some detail. In the second chapter we show how to solve wave equations locally. Using Riesz distributions and a formal recursive procedure