scholarly journals Algebraic QFT in Curved Spacetime and Quasifree Hadamard States: An Introduction

2015 ◽  
pp. 191-251 ◽  
Author(s):  
Igor Khavkine ◽  
Valter Moretti
Keyword(s):  
Curved Spacetime ◽  
Hadamard States ◽  
Algebraic Qft

scholarly journals DYNAMICAL BACKREACTION IN ROBERTSON–WALKER SPACETIME

2011 ◽  
Vol 23 (05) ◽  
pp. 531-551 ◽  
Author(s):  
BENJAMIN ELTZNER ◽  
HANNO GOTTSCHALK
Keyword(s):  
Dynamical System ◽  
Scalar Field ◽  
Stress Tensor ◽  
Einstein Equation ◽  
Scale Parameter ◽  
The State ◽  
Curved Spacetime ◽  
Free Scalar ◽  
Hadamard States ◽  
Quantized Field

The treatment of a quantized field in a curved spacetime requires the study of backreaction of the field on the spacetime via the semiclassical Einstein equation. We consider a free scalar field in spatially flat Robertson–Walker spacetime. We require the state of the field to allow for a renormalized semiclassical stress tensor. We calculate the singularities of the stress tensor restricted to equal times in agreement with the usual renormalization prescription for Hadamard states to perform an explicit renormalization. The dynamical system for the Robertson–Walker scale parameter a(t) coupled to the scalar field is finally derived for the case of conformal and also general coupling.

scholarly journals On the global Hadamard parametrix in QFT and the signed squared geodesic distance defined in domains larger than convex normal neighbourhoods

2021 ◽  
Vol 111 (5) ◽  
Author(s):  
Valter Moretti
Keyword(s):  
Geodesic Distance ◽  
Technical Problem ◽  
Open Neighbourhood ◽  
Curved Spacetime ◽  
Main Text ◽  
Hadamard Condition ◽  
Original Definition ◽  
Natural Solution ◽  
Definition Of ◽  
Algebraic Qft

AbstractWe consider the global Hadamard condition and the notion of Hadamard parametrix whose use is pervasive in algebraic QFT in curved spacetime (see references in the main text). We point out the existence of a technical problem in the literature concerning well-definedness of the global Hadamard parametrix in normal neighbourhoods of Cauchy surfaces. We discuss in particular the definition of the (signed) geodesic distance $$\sigma $$ σ and related structures in an open neighbourhood of the diagonal of $$M\times M$$ M × M larger than $$U\times U$$ U × U , for a normal convex neighbourhood U, where (M, g) is a Riemannian or Lorentzian (smooth Hausdorff paracompact) manifold. We eventually propose a quite natural solution which slightly changes the original definition by Kay and Wald and relies upon some non-trivial consequences of the paracompactness property. The proposed re-formulation is in agreement with Radzikowski’s microlocal version of the Hadamard condition.

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.

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.

GRAVITY CAN BE OBSERVED IN THE ABSENCE OF CURVED SPACETIME, THUS CURVED SPACETIME IS NOT RESPONCIBLE FOR GRAVITY

2015 ◽  
Vol 8 (1) ◽  
pp. 1976-1981
Author(s):  
Casey McMahon
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Relative Position ◽  
Gravitational Force ◽  
Curved Spacetime ◽  
Relative Time ◽  
Curved Space ◽  
Spacetime Curvature ◽  
Equivalence Model ◽  
The Universe

The principle postulate of general relativity appears to be that curved space or curved spacetime is gravitational, in that mass curves the spacetime around it, and that this curved spacetime acts on mass in a manner we call gravity. Here, I use the theory of special relativity to show that curved spacetime can be non-gravitational, by showing that curve-linear space or curved spacetime can be observed without exerting a gravitational force on mass to induce motion- as well as showing gravity can be observed without spacetime curvature. This is done using the principles of special relativity in accordance with Einstein to satisfy the reader, using a gravitational equivalence model. Curved spacetime may appear to affect the apparent relative position and dimensions of a mass, as well as the relative time experienced by a mass, but it does not exert gravitational force (gravity) on mass. Thus, this paper explains why there appears to be more gravity in the universe than mass to account for it, because gravity is not the resultant of the curvature of spacetime on mass, thus the “dark matter” and “dark energy” we are looking for to explain this excess gravity doesn’t exist.

Creation of vector bosons by an electric field in curved spacetime

2014 ◽  
Vol 343 ◽  
pp. 40-48 ◽  
Author(s):  
E. Ersin Kangal ◽  
Hilmi Yanar ◽  
Ali Havare ◽  
Kenan Sogut
Keyword(s):  
Electric Field ◽  
Curved Spacetime ◽  
Vector Bosons

RENORMALIZATION GROUP AND WORMHOLES

1992 ◽  
Vol 01 (02) ◽  
pp. 401-405 ◽  
Author(s):  
S.D. ODINTSOV ◽  
J. PEREZ-MERCADER
Keyword(s):  
Renormalization Group ◽  
Cosmological Constant ◽  
Curved Spacetime ◽  
Curved Space

We incorporate the curved spacetime renormalization group into Coleman’s analysis of cosmological constant vanishing in the framework of wormholes. It is shown that for asymptotically free or finite GUT’s in curved space, Coleman’s mechanism can be realized.

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