scholarly journals SCALING LIMITS OF INTEGRABLE QUANTUM FIELD THEORIES

2011 ◽  
Vol 23 (10) ◽  
pp. 1115-1156 ◽  
Author(s):  
HENNING BOSTELMANN ◽  
GANDALF LECHNER ◽  
GERARDO MORSELLA
Keyword(s):  
Scaling Limit ◽  
Field Theories ◽  
Scaling Limits ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Möbius Group ◽  
Dimensional Minkowski Space ◽  
Local Quantum ◽  
Algebraic Framework ◽  
Covariant Field

Short distance scaling limits of a class of integrable models on two-dimensional Minkowski space are considered in the algebraic framework of quantum field theory. Making use of the wedge-local quantum fields generating these models, it is shown that massless scaling limit theories exist, and decompose into (twisted) tensor products of chiral, translation-dilation covariant field theories. On the subspace which is generated from the vacuum by the observables localized in finite light ray intervals, this symmetry can be extended to the Möbius group. The structure of the interval-localized algebras in the chiral models is discussed in two explicit examples.

scholarly journals A thermodynamic origin for the Cohen-Kaplan-Nelson bound

2021 ◽  
Author(s):  
Satish Ramakrishna
Keyword(s):  
General Relativity ◽  
Free Energy ◽  
Equation Of State ◽  
Density Of States ◽  
Canonical Ensemble ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Local Quantum ◽  
The Universe

Abstract The Cohen-Kaplan-Nelson bound is imposed on the grounds of logical consistency (with classical General Relativity) upon local quantum field theories. This paper puts the bound into the context of a thermodynamic principle applicable to a field with a particular equation of state in an expanding universe. This is achieved without overtly appealing to either a decreasing density of states or a minimum coupling requirement, though they might still be consistent with the results described. The paper establishes that the holographic principle applied to cosmology is consistent with minimizing the free energy of the universe in the canonical ensemble, upon the assumption that the ultraviolet cutoff is a function of the causal horizon scale.

RAINBOW STATISTICS

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4623-4641 ◽  
Author(s):  
MICHELE ARZANO ◽  
DARIO BENEDETTI
Keyword(s):  
Quantum Group ◽  
Hilbert Spaces ◽  
Group Symmetry ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Additional Structure ◽  
Local Quantum ◽  
Group Symmetries ◽  
Noncommutative Quantum

Noncommutative quantum field theories and their global quantum group symmetries provide an intriguing attempt to go beyond the realm of standard local quantum field theory. A common feature of these models is that the quantum group symmetry of their Hilbert spaces induces additional structure in the multiparticle states which reflects a nontrivial momentum-dependent statistics. We investigate the properties of this "rainbow statistics" in the particular context of κ-quantum fields and discuss the analogies/differences with models with twisted statistics.

SUPERSELECTION STRUCTURE AND LOCALIZED CONNES’ COCYCLES

1995 ◽  
Vol 07 (01) ◽  
pp. 133-160 ◽  
Author(s):  
HANS-WERNER WIESBROCK
Keyword(s):  
Field Theories ◽  
Local Theory ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Localization Property ◽  
Algebra Of Observables ◽  
Local Algebras ◽  
Möbius Group ◽  
Modular Groups

Let ρ be a localized endomorphism of the universal algebra of observables of a chiral conformal quantum field theory on a circle, see [16, 17, 23] or Chapter 1. Then ρ transforms covariant under the Möbius group. As was pointed out by D. Guido and R. Longo, [23], the covariance transformations are implemented by [Formula: see text] where Ad ∆it are modular groups to local algebras w.r.t. the vacuum vector, ut is a Connes-Radon-Nikodym-Cocycle. Using the localization property of ρ, one gets, at least for regular nets, localization properties of the cocycles. In this work we will do some steps into the opposite direction. Given a localized Connes’ cocycle of a local algebra. We will construct a localized endomorphism on the whole net. The features of this approach are twofold. Firstly sectors of finite and infinite statistical dimensions are handled on the same footing. Secondly it is a local theory right from the beginning. Moreover, soliton-like sectors can easily be incorporated. We will sketch on the last part. The program is carried through for a special class of conformal quantum field theories, the strongly additive ones.

scholarly journals A thermodynamic origin for the Cohen-Kaplan-Nelson bound

2021 ◽  
Author(s):  
Satish Ramakrishna
Keyword(s):  
General Relativity ◽  
Free Energy ◽  
Equation Of State ◽  
Density Of States ◽  
Canonical Ensemble ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Local Quantum ◽  
The Universe

Abstract The Cohen-Kaplan-Nelson bound is imposed on the grounds of logical consistency (with classical General Relativity) upon local quantum field theories. This paper puts the bound into the context of a thermodynamic principle applicable to a field with a particular equation of state in an expanding universe. This is achieved without overtly appealing to either a decreasing density of states or a minimum coupling requirement, though they might still be consistent with the results described. The paper establishes that the holographic principle applied to cosmology is consistent with minimizing the free energy of the universe in the canonical ensemble, upon the assumption that the ultraviolet cutoff is a function of the causal horizon scale.

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