scholarly journals Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes

2022 ◽  
Vol 63 (1) ◽  
pp. 013501
Author(s):  
Max Lewandowski
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Globally Hyperbolic ◽  
Globally Hyperbolic Spacetimes ◽  
Hadamard States ◽  
Hyperbolic Spacetimes

THE PRINCIPLE OF LOCALITY AND QUANTUM FIELD THEORY ON (NON GLOBALLY HYPERBOLIC) CURVED SPACETIMES

1992 ◽  
Vol 04 (spec01) ◽  
pp. 167-195 ◽  
Author(s):  
BERNARD S. KAY
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Field Algebra ◽  
Massless Field ◽  
Globally Hyperbolic ◽  
Local Algebras ◽  
Hyperbolic Spacetime ◽  
Globally Hyperbolic Spacetimes ◽  
Hyperbolic Spacetimes

In the context of a linear model (the covariant Klein Gordon equation) we review the mathematical and conceptual framework of quantum field theory on globally hyperbolic spacetimes, and address the question of what it might mean to quantize a field on a non globally hyperbolic spacetime. Our discussion centres on the notion of F-locality which we introduce and which asserts there is a net of local algebras such that every neighbourhood of every point contains a globally hyperbolic subneighbourhood of that point for which the field algebra coincides with the algebra one would obtain were one to regard the subneighbourhood as a spacetime in its own right and quantize — with some choice of time-orientation — according to the standard rules for quantum field theory on globally hyperbolic spacetimes. We show that F-locality is a property of the standard field algebra construction for globally hyperbolic spacetimes, and argue that it (or something similar) should be imposed as a condition on any field algebra construction for non globally hyperbolic spacetimes. We call a spacetime for which there exists a field algebra satisfying F-locality F-quantum compatible and argue that a spacetime which did not satisfy something similar to this condition could not arise as an approximate classical description of a state of quantum gravity and would hence be ruled out physically. We show that all F-quantum compatible spacetimes are time orientable. We also raise the issue of whether chronology violating spacetimes can be F-quantum compatible, giving a special model — a massless field theory on the “four dimensional spacelike cylinder” — which is F-quantum compatible, and a (two dimensional) model — a massless field theory on Misner space — which is not. We discuss the possible relevance of this latter result to Hawking’s recent Chronology Protection Conjecture.

scholarly journals The locality axiom in quantum field theory and tensor products of C*-algebras

2014 ◽  
Vol 26 (06) ◽  
pp. 1450010 ◽  
Author(s):  
Romeo Brunetti ◽  
Klaus Fredenhagen ◽  
Paniz Imani ◽  
Katarzyna Rejzner
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Local Observable ◽  
Quantum Field ◽  
Covariant Quantum ◽  
C Algebras ◽  
Local Algebras ◽  
Globally Hyperbolic Spacetimes ◽  
Split Property ◽  
Hyperbolic Spacetimes

The prototypes of mutually independent systems are systems which are localized in spacelike separated regions. In the framework of locally covariant quantum field theory, we show that the commutativity of observables in spacelike separated regions can be encoded in the tensorial structure of the functor which associates unital C*-algebras (the local observable algebras) to globally hyperbolic spacetimes. This holds under the assumption that the local algebras satisfy the split property and involves the minimal tensor product of C*-algebras.

scholarly journals CHARGED SECTORS, SPIN AND STATISTICS IN QUANTUM FIELD THEORY ON CURVED SPACETIMES

2001 ◽  
Vol 13 (02) ◽  
pp. 125-198 ◽  
Author(s):  
D. GUIDO ◽  
R. LONGO ◽  
J. E. ROBERTS ◽  
R. VERCH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Holes ◽  
Rotational Symmetry ◽  
Minkowski Spacetime ◽  
Rotation Group ◽  
Quantum Field ◽  
Covariant Quantum ◽  
Killing Horizon ◽  
Hyperbolic Spacetimes

The first part of this paper extends the Doplicher–Haag–Roberts theory of superselection sectors to quantum field theory on arbitrary globally hyperbolic spacetimes. The statistics of a superselection sector may be defined as in flat spacetime and each charge has a conjugate charge when the spacetime possesses non-compact Cauchy surfaces. In this case, the field net and the gauge group can be constructed as in Minkowski spacetime. The second part of this paper derives spin-statistics theorems on spacetimes with appropriate symmetries. Two situations are considered: First, if the spacetime has a bifurcate Killing horizon, as is the case in the presence of black holes, then restricting the observables to the Killing horizon together with "modular covariance" for the Killing flow yields a conformally covariant quantum field theory on the circle and a conformal spin-statistics theorem for charged sectors localizable on the Killing horizon. Secondly, if the spacetime has a rotation and PT symmetry like the Schwarzschild–Kruskal black holes, "geometric modular action" of the rotational symmetry leads to a spin-statistics theorem for charged covariant sectors where the spin is defined via the SU(2)-covering of the spatial rotation group SO(3).

scholarly journals Partial Differential Equations and Quantum States in Curved Spacetimes

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1936
Author(s):  
Zhirayr Avetisyan ◽  
Matteo Capoferri
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Review Paper ◽  
Quantum States ◽  
Quantum Field ◽  
Partial Differential ◽  
Curved Spacetimes ◽  
Globally Hyperbolic Spacetimes ◽  
Hadamard States ◽  
Hyperbolic Spacetimes

In this review paper, we discuss the relation between recent advances in the theory of partial differential equations and their applications to quantum field theory on curved spacetimes. In particular, we focus on hyperbolic propagators and the role they play in the construction of physically admissible quantum states—the so-called Hadamard states—on globally hyperbolic spacetimes. We will review the notion of a propagator and discuss how it can be constructed in an explicit and invariant fashion, first on a Riemannian manifold and then on a Lorentzian spacetime. Finally, we will recall the notion of Hadamard state and relate the latter to hyperbolic propagators via the wavefront set, a subset of the cotangent bundle capturing the information about the singularities of a distribution.

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