The structure of local algebras in quantum field theory

2008 ◽  
pp. 79-90
Author(s):  
D. Buchholz
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Local Algebras

scholarly journals Generic Bell correlation between arbitrary local algebras in quantum field theory

2000 ◽  
Vol 41 (4) ◽  
pp. 1711-1717 ◽  
Author(s):  
Hans Halvorson ◽  
Rob Clifton
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Local Algebras

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.

ENTROPY DENSITY FOR RELATIVISTIC QUANTUM FIELD THEORY

1994 ◽  
Vol 06 (05a) ◽  
pp. 1127-1145 ◽  
Author(s):  
HEIDE NARNHOFER
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Ground State ◽  
Relativistic Quantum ◽  
Entropy Density ◽  
Quantum Field ◽  
Local Entropy ◽  
Relativistic Quantum Field Theory ◽  
Local Algebras ◽  
Nuclearity Condition

We show how the nuclearity condition of Buchholz and Wichmann allows to define in the ground state a local entropy with the desired properties despite the fact that local algebras are type III. Generalization to temperature states is also possible so that thermodynamic functions also exist in the context of relativistic quantum field theory.

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 GEOMETRIC MODULAR ACTION FOR DISJOINT INTERVALS AND BOUNDARY CONFORMAL FIELD THEORY

2010 ◽  
Vol 22 (03) ◽  
pp. 331-354 ◽  
Author(s):  
ROBERTO LONGO ◽  
PIERRE MARTINETTI ◽  
KARL-HENNING REHREN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Modular Group ◽  
Vacuum State ◽  
Quantum Field ◽  
Conformal Field ◽  
Local Algebras

In suitable states, the modular group of local algebras associated with unions of disjoint intervals in chiral conformal quantum field theory acts geometrically. We translate this result into the setting of boundary conformal QFT and interpret it as a relation between temperature and acceleration. We also discuss novel aspects ("mixing" and "charge splitting") of geometric modular action for unions of disjoint intervals in the vacuum state.

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