On the status of pointlike fields in integrable QFTs

Henning Bostelmann

doi:10.1088/1742-6596/1416/1/012006

On the status of pointlike fields in integrable QFTs

Henning Bostelmann

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In integrable models of quantum field theory, local fields are normally constructed by means of the bootstrap-formfactor program. However, the convergence of their n-point functions is unclear in this setting. An alternative approach uses fully convergent expressions for fields with weaker localization properties in spacelike wedges, and deduces existence of observables in bounded regions from there, but yields little information about their explicit form. We propose a new, hybrid construction: We aim to describe pointlike local quantum fields; but rather than exhibiting their n-point functions and verifying the Wightman axioms, we establish them as closed operators affiliated with a net of local von Neumann algebras that is known from the wedge-local approach. This is shown to work at least in the Ising model.

Original language	English
Title of host publication	XXVI International Conference on Integrable Systems and Quantum symmetries
Volume	1416
DOIs	https://doi.org/10.1088/1742-6596/1416/1/012006
Publication status	Published - 16 Dec 2019

Publication series

Name	Journal of Physics: Conference Series
Publisher	IOP
Volume	1416

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10.1088/1742-6596/1416/1/012006Licence: CC BY

Bostelmann_2019_J._Phys.__Conf._Ser._1416_012006
© 2019, The Author(s).
Final published version, 628 KBLicence: CC BY

1 Talk

On the status of pointlike fields in integrable QFTs
Henning Bostelmann (Speaker)
10 Jul 2019
Activity: Talk or presentation › Talk

Cite this

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title = "On the status of pointlike fields in integrable QFTs",

abstract = "In integrable models of quantum field theory, local fields are normally constructed by means of the bootstrap-formfactor program. However, the convergence of their n-point functions is unclear in this setting. An alternative approach uses fully convergent expressions for fields with weaker localization properties in spacelike wedges, and deduces existence of observables in bounded regions from there, but yields little information about their explicit form. We propose a new, hybrid construction: We aim to describe pointlike local quantum fields; but rather than exhibiting their n-point functions and verifying the Wightman axioms, we establish them as closed operators affiliated with a net of local von Neumann algebras that is known from the wedge-local approach. This is shown to work at least in the Ising model.",

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N2 - In integrable models of quantum field theory, local fields are normally constructed by means of the bootstrap-formfactor program. However, the convergence of their n-point functions is unclear in this setting. An alternative approach uses fully convergent expressions for fields with weaker localization properties in spacelike wedges, and deduces existence of observables in bounded regions from there, but yields little information about their explicit form. We propose a new, hybrid construction: We aim to describe pointlike local quantum fields; but rather than exhibiting their n-point functions and verifying the Wightman axioms, we establish them as closed operators affiliated with a net of local von Neumann algebras that is known from the wedge-local approach. This is shown to work at least in the Ising model.

AB - In integrable models of quantum field theory, local fields are normally constructed by means of the bootstrap-formfactor program. However, the convergence of their n-point functions is unclear in this setting. An alternative approach uses fully convergent expressions for fields with weaker localization properties in spacelike wedges, and deduces existence of observables in bounded regions from there, but yields little information about their explicit form. We propose a new, hybrid construction: We aim to describe pointlike local quantum fields; but rather than exhibiting their n-point functions and verifying the Wightman axioms, we establish them as closed operators affiliated with a net of local von Neumann algebras that is known from the wedge-local approach. This is shown to work at least in the Ising model.

U2 - 10.1088/1742-6596/1416/1/012006

DO - 10.1088/1742-6596/1416/1/012006

M3 - Conference contribution

VL - 1416

T3 - Journal of Physics: Conference Series

BT - XXVI International Conference on Integrable Systems and Quantum symmetries

ER -

On the status of pointlike fields in integrable QFTs

Abstract

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On the status of pointlike fields in integrable QFTs

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