Deformations of quantum field theories on spacetimes with Killing vector fields

Claudio Dappiaggi; Eric Morfa-Morales; Gandalf Lechner

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Deformations of quantum field theories on spacetimes with Killing vector fields

Claudio Dappiaggi, Gandalf Lechner, Eric Morfa-Morales

Mathematical Physics · Submitted 17 Jun 2010

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The authors' main claim The recent construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of curved spacetimes.

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arXiv ID1006.3548 (version 1)

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CitationClaudio Dappiaggi, Eric Morfa-Morales, Gandalf Lechner. "Deformations of quantum field theories on spacetimes with Killing vector fields." arXiv:1006.3548 (2010). https://pith.science/paper/E3KF6VIC

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.52 · mentions code or data availability 0.01.

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The recent construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of curved spacetimes. These spacetimes carry a family of wedge-like regions which share the essential causal properties of the Poincare transforms of the Rindler wedge in Minkowski space. In the setting of deformed quantum field theories, they play the role of typical localization regions of quantum fields and observables. As a concrete example of such a procedure, the deformation of the free Dirac field is studied.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The recent construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of curved spacetimes.	contribution 0.99	0.70	0.30	asserted 1.00
s1	These spacetimes carry a family of wedge-like regions which share the essential causal properties of the Poincare transforms of the Rindler wedge in Minkowski space.	contribution 0.55	0.38	0.08	asserted 1.00
s2	In the setting of deformed quantum field theories, they play the role of typical localization regions of quantum fields and observables.	interpretation 0.56	0.21	0.09	asserted 1.00
s3	As a concrete example of such a procedure, the deformation of the free Dirac field is studied.	contribution 0.84	0.86	0.08	asserted 0.98

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Original abstract

The recent construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of curved spacetimes. These spacetimes carry a family of wedge-like regions which share the essential causal properties of the Poincare transforms of the Rindler wedge in Minkowski space. In the setting of deformed quantum field theories, they play the role of typical localization regions of quantum fields and observables. As a concrete example of such a procedure, the deformation of the free Dirac field is studied.

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9 arXiv papers cite this in 20 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 14 sentences without a confident label

Uses its method or tool 1 paper

We proceed in a similar manner as in [ref] .

Deformations of quantum field theories on de Sitter spacetime · Unitary inequivalence · 0.99

Compares with it 1 paper

The deformation scheme in this paper is very different from the one in [ref] , where the Killing flow associated with the edge of a wedge was used to formulate the deformation.

Deformations of quantum field theories on de Sitter spacetime · Conclusion and outlook · 1.00

Cites it as background 4 papers

We recall that a new class of relativistic quantum field theories, including both massive and massless models, has been obtained recently by a certain deformation procedure akin to the Rieffel deformation [ref] .

Asymptotic completeness in a class of massless relativistic quantum field theories · Introduction · 0.85
The construction of interacting quantum field theories by deformations using suitable actions of $^n$ has recently attracted much attention [ref] , [ref] , [ref] , [ref] , [ref] , [ref] .

Deformations of quantum field theories on de Sitter spacetime · Introduction · 0.98
Wedge local deformations of QFTs on curved spacetimes by Killing vector fields and Rieffel products have been studied in [ref] .

QFT on homothetic Killing twist deformed curved spacetimes · Introduction · 0.95

What it cites · 43 sentences without a confident label

Builds on 1 paper

For models on flat Minkowski space, it is known that this deformation procedure weakens point-like localization to localization in wedges [ref] , and we will show here that the same holds true for admissible curved spacetimes.

Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories · Quantum field theories on admissible spacetimes · 0.84

Uses the method or tool of 4 papers

In this setting, all structural elements necessary for the application of warped convolution deformations [ref] are present, and we will use this technique to define a deformed net $W⟼(W)_$ of $C^*$-algebras on $M$, depending on a deformation parameter $∈$.

Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories · Deformations of nets with Killing symmetries · 0.88
A deformation technique which is well suited for our purposes is that of warped convolutions, see [ref] and [ref] for precursors and related work.

Wedge-Local Quantum Fields and Noncommutative Minkowski Space · Introduction · 0.87
A deformation technique which is well suited for our purposes is that of warped convolutions, see [ref] and [ref] for precursors and related work.

Warped Convolutions: A Novel Tool in the Construction of Quantum Field Theories · Introduction · 0.87

Compares with 5 papers

They therefore depend on the sign convention in the metric signature, and differ from those introduced in [ref] , where a different convention was used.

The extended algebra of observables for Dirac fields and the trace anomaly of their stress-energy tensor · The Dirac field and its deformation · 0.91
At the end of that section, we compare our notion of wedges to other definitions which have been made in the literature [ref] , and point out the similarities and differences.

Structural and Dynamical Aspects of the AdS/CFT Correspondence: a Rigorous Approach · Geometric setup · 0.98
At the end of that section, we compare our notion of wedges to other definitions which have been made in the literature [ref] , and point out the similarities and differences.

Global Properties of Vacuum States in de Sitter Space · Geometric setup · 0.98

Cites as background 24 papers

In fact, different definitions are possible, and wedges on special manifolds have been studied by many authors in the literature [ref] .

Structural and Dynamical Aspects of the AdS/CFT Correspondence: a Rigorous Approach · Introduction · 0.87
In fact, different definitions are possible, and wedges on special manifolds have been studied by many authors in the literature [ref] .

Transplantation of Local Nets and Geometric Modular Action on Robertson-Walker Space-Times · Introduction · 0.87
In fact, different definitions are possible, and wedges on special manifolds have been studied by many authors in the literature [ref] .

Algebraic Holography · Introduction · 0.87

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