Wedge-local quantum fields on a nonconstant noncommutative spacetime

Much, Albert

doi:10.1063/1.4739751

Cited by 13 publications

(13 citation statements)

References 27 publications

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“…In [15] we investigated how to obtain a non-commutative spacetime from coordinate operators. The investigation in this case was guided by physical intuition.…”

Section: Applicationsmentioning

confidence: 99%

Preconjugate variables in quantum field theory and their applications

2016

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Preconjugate variables X have commutation relations with the energy-momentum P of the respective system which are of a more general form than just the Hamiltonian one. Since they have been proven useful in their own right for finding new spacetimes we present here a study of them. Interesting examples can be found via geometry: motions on the mass-shell for massive and massless systems, and via group theory: invariance under special conformal transformations of mass-shell, resp. light-cone -both find representations on Fock space. We work mainly in ordinary fourdimensional Minkowski space and spin zero. The limit process from non-zero to vanishing mass turns out to be non-trivial and leads naturally to wedge variables. We point out some applications and extension to more general spacetimes. In a companion paper we discuss the transition to conjugate pairs. 1

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“…In [15] we investigated how to obtain a non-commutative spacetime from coordinate operators. The investigation in this case was guided by physical intuition.…”

Section: Applicationsmentioning

confidence: 99%

Preconjugate variables in quantum field theory and their applications

2016

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“…31 Some familiar quantum-mechanical effects were reproduced in Ref. 32 by deforming some initial free operators into the desired ones.…”

Section: Operator Deformationsmentioning

confidence: 99%

“…The formula (1.2) has interesting applications in physics, for example when the generators are the momenta P µ but other commuting generators can also be important [Mu2]. Some familiar quantummechanical effects where reproduced in [Mu1] by deforming some initial free operators into the desired ones.…”

Section: Operator Deformationsmentioning

confidence: 99%

Electromagnetism in terms of quantum measurements

Andersson

2016

Journal of Mathematical Physics

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We consider the question whether electromagnetism can be derived from the theory of quantum measurements. It turns out that this is possible, both for quantum and classical electromagnetism, if we use more recent innovations such as smearing of observables and simultaneous measurability. In this way, we justify the use of von Neumann-type measurement models for physical processes. We apply the operational quantum measurement theory to gain insight into fundamental aspects of quantum physics. Interactions of von Neumann type make the Heisenberg evolution of observables describable using explicit operator deformations. In this way, one can obtain quantized electromagnetism as a measurement of a system by another. The relevant deformations (Rieffel deformations) have a mathematically well-defined "classical" limit which is indeed classical electromagnetism for our choice of interaction. Disciplines Engineering | Science and Technology StudiesPublication Details Andersson, A. (2016 We consider the question whether electromagnetism can be derived from the theory of quantum measurements. It turns out that this is possible, both for quantum and classical electromagnetism, if we use more recent innovations such as smearing of observables and simultaneous measurability. In this way, we justify the use of von Neumann-type measurement models for physical processes. We apply the operational quantum measurement theory to gain insight into fundamental aspects of quantum physics. Interactions of von Neumann type make the Heisenberg evolution of observables describable using explicit operator deformations. In this way, one can obtain quantized electromagnetism as a measurement of a system by another. The relevant deformations (Rieffel deformations) have a mathematically well-defined "classical" limit which is indeed classical electromagnetism for our choice of interaction. Published by AIP Publishing. [http://dx

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“…In recent years, there has been a lot of interest in deformations of quantum field theories [1,3,[8][9][10]12,[17][18][19][20][21][22]24] in the sense of specific procedures modifying quantum field theoretic models on Minkowski space, mostly motivated by the desire to construct new models in a non-perturbative manner. Various constructions have been invented, relying on different methods such as smooth group actions, noncommutative geometry, chiral conformal field theory, boundary quantum field theory, and inverse scattering theory.…”

Section: Deformations Of Qfts By Inner Functions and Their Rootsmentioning

confidence: 99%

On the Equivalence of Two Deformation Schemes in Quantum Field Theory

2012

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Abstract. Two recent deformation schemes for quantum field theories on two-dimensional Minkowski space, making use of deformed field operators and Longo-Witten endomorphisms, respectively, are shown to be equivalent. Mathematics Subject Classification (2010). 81T05, 81T40.Keywords. deformations of quantum field theories, two-dimensional models, modular theory. Deformations of QFTs by Inner Functions and Their RootsIn recent years, there has been a lot of interest in deformations of quantum field theories [1,3,[8][9][10]12,[17][18][19][20][21][22]24] in the sense of specific procedures modifying quantum field theoretic models on Minkowski space, mostly motivated by the desire to construct new models in a non-perturbative manner. Various constructions have been invented, relying on different methods such as smooth group actions, noncommutative geometry, chiral conformal field theory, boundary quantum field theory, and inverse scattering theory.In many situations, it is possible to set up the deformation in such a way that Poincaré covariance is completely preserved and locality partly. More precisely, often the deformation introduces operators which are no longer localized in arbitrarily small regions of spacetime, but rather in unbounded regions like a Rindler wedge W := {x ∈ R d : x 1 > |x 0 |}. In the operator-algebraic framework of quantum field theory [14], such a wedge-local Poincaré covariant model can be conveniently described by a so-called Borchers triple (M, U, ) [4,8], consisting of a GL and JS supported by FWF project P22929-N16 "Deformations of quantum field theories". Y. Tanimoto supported by Deutscher Akademischer Austauschdienst.

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Wedge-local quantum fields on a nonconstant noncommutative spacetime

Cited by 13 publications

References 27 publications

Preconjugate variables in quantum field theory and their applications

Preconjugate variables in quantum field theory and their applications

Electromagnetism in terms of quantum measurements

On the Equivalence of Two Deformation Schemes in Quantum Field Theory

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