scholarly journals ERRATUM TO "HADAMARD STATES, ADIABATIC VACUA AND THE CONSTRUCTION OF PHYSICAL STATES FOR SCALAR QUANTUM FIELDS ON CURVED SPACETIME"

2002 ◽  
Vol 14 (05) ◽  
pp. 511-517 ◽  
Author(s):  
WOLFGANG JUNKER
Keyword(s):  
Quantum Fields ◽  
Curved Spacetime ◽  
Scalar Quantum ◽  
Hadamard States ◽  
Math Phys

In this erratum we want to correct or modify some of the original statements and proofs in "Hadamard States, Adiabatic Vacua and the Construction of Physical States for Scalar Quantum Fields on Curved Spacetime" in Rev. Math. Phys. 8 (1996) 1091–1159.

scholarly journals MICROLOCAL SPECTRUM CONDITION AND HADAMARD FORM FOR VECTOR-VALUED QUANTUM FIELDS IN CURVED SPACETIME

2001 ◽  
Vol 13 (10) ◽  
pp. 1203-1246 ◽  
Author(s):  
HANNO SAHLMANN ◽  
RAINER VERCH
Keyword(s):  
Vector Bundle ◽  
Scalar Fields ◽  
Quantum Fields ◽  
Curved Spacetime ◽  
Globally Hyperbolic ◽  
Commutation Relations ◽  
Hyperbolic Spacetime ◽  
Hadamard Condition ◽  
Spectrum Condition ◽  
Hadamard States

Some years ago, Radzikowski has found a characterization of Hadamard states for scalar quantum fields on a four-dimensional globally hyperbolic spacetime in terms of a specific form of the wavefront set of their two-point functions (termed "wavefront set spectrum condition"), thereby initiating a major progress in the understanding of Hadamard states and the further development of quantum field theory in curved spacetime. In the present work, we extend this important result on the equivalence of the wavefront set spectrum condition with the Hadamard condition from scalar fields to vector fields (sections in a vector bundle) which are subject to a wave-equation 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 anti-commutation 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 short-distance saling limits of Hadamard states for vector-bundle valued fields, finding them to coincide with the corresponding flat-space, massless vacuum states.

Estimates on Renormalization Group Transformations

1998 ◽  
Vol 50 (4) ◽  
pp. 756-793 ◽  
Author(s):  
D. Brydges ◽  
J. Dimock ◽  
T. R. Hurd
Keyword(s):  
Renormalization Group ◽  
Gaussian Measure ◽  
Ultra Violet ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Quantum Fields ◽  
Scalar Quantum ◽  
Polymer Expansion ◽  
Renormalization Group Flows

AbstractWe consider a specific realization of the renormalization group (RG) transformation acting on functional measures for scalar quantum fields which are expressible as a polymer expansion times an ultra-violet cutoff Gaussian measure. The new and improved definitions and estimates we present are sufficiently general and powerful to allow iteration of the transformation, hence the analysis of complete renormalization group flows, and hence the construction of a variety of scalar quantum field theories.

scholarly journals Quantum Fields in Curved Spacetime

2015 ◽  
pp. 513-552 ◽  
Author(s):  
Stefan Hollands ◽  
Robert M. Wald
Keyword(s):  
Quantum Fields ◽  
Curved Spacetime

Scaling behavior of interacting quantum fields in curved spacetime

1982 ◽  
Vol 25 (4) ◽  
pp. 1019-1027 ◽  
Author(s):  
Bruce L. Nelson ◽  
Prakash Panangaden
Keyword(s):  
Scaling Behavior ◽  
Quantum Fields ◽  
Curved Spacetime

HADAMARD STATES, ADIABATIC VACUA AND THE CONSTRUCTION OF PHYSICAL STATES FOR SCALAR QUANTUM FIELDS ON CURVED SPACETIME

1996 ◽  
Vol 08 (08) ◽  
pp. 1091-1159 ◽  
Author(s):  
WOLFGANG JUNKER
Keyword(s):  
Pseudodifferential Operators ◽  
Cauchy Surface ◽  
Positive Energy ◽  
Hyperbolic Spacetime ◽  
Vacuum States ◽  
Mathematical Review ◽  
Scalar Quantum ◽  
Klein Gordon ◽  
Hadamard States ◽  
Adiabatic Vacuum

Quasifree states of a linear Klein-Gordon quantum field on globally hyperbolic spacetime manifolds are considered. After a short mathematical review techniques from the theory of pseudodifferential operators and wavefront sets on manifolds are used to develop a criterion for a state to be an Hadamard state. It is proven that ground- and KMS-states on certain static spacetimes and adiabatic vacuum states on Robertson-Walker spaces are Hadamard states. A counterexample is given which shows that the idea of instantaneous positive energy states w.r.t. a Cauchy surface does in general not yield physical states. Finally, the problem of constructing Hadamard states on arbitrary curved spacetimes is solved in principle.

Quantum fields as Cosmic Censors in (2 + 1)-dimensions

2018 ◽  
Vol 27 (11) ◽  
pp. 1843011 ◽  
Author(s):  
Marc Casals ◽  
Alessandro Fabbri ◽  
Cristián Martínez ◽  
Jorge Zanelli
Keyword(s):  
Black Hole ◽  
Naked Singularity ◽  
Quantum Effects ◽  
Conical Singularity ◽  
Cauchy Horizon ◽  
Quantum Fields ◽  
Rotating Black Hole ◽  
Scalar Quantum ◽  
Do So ◽  
Classical Background

We discuss the effect of quantum fields on classical background spacetimes which contain timelike singularities. We do so for the case that the background is a [Formula: see text]-dimensional BTZ spacetime, whether corresponding to a rotating black hole ([Formula: see text]) or to a naked conical singularity ([Formula: see text]). In the black hole case, scalar quantum fields render its Cauchy horizon unstable, while for the conical geometry, they produce a horizon around the naked singularity. Thus, quantum effects improve the predictability of the spacetime acting as effective Cosmic Censors.

Nonstandard scalar quantum fields

1994 ◽  
Vol 35 (8) ◽  
pp. 3817-3844 ◽  
Author(s):  
Stanley Gudder
Keyword(s):  
Quantum Fields ◽  
Scalar Quantum
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