Inverse Scattering and Local Observable Algebras in Integrable Quantum Field Theories

We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S -matrix. An arbitrary number of massive particles transforming under an arbitrary com...

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Bibliographic Details
Published in:Communications in mathematical physics Vol. 354; no. 3; pp. 913 - 956
Main Authors: Alazzawi, Sabina, Lechner, Gandalf
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2017
Springer Nature B.V
Subjects:
Algebra
Classical and Quantum Gravitation
Complex Systems
Identification methods
Invariance
Inverse scattering
Mathematical and Computational Physics
Mathematical Physics
Matrices (mathematics)
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
ISSN:0010-3616, 1432-0916
Online Access:Get full text
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Summary:We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S -matrix. An arbitrary number of massive particles transforming under an arbitrary compact global gauge group is allowed, thereby generalizing previous constructions of scalar theories. The two-particle S -matrix S is assumed to be an analytic solution of the Yang–Baxter equation with standard properties, including unitarity, TCP invariance, and crossing symmetry. Using methods from operator algebras and complex analysis, we identify sufficient criteria on S that imply the solution of the inverse scattering problem. These conditions are shown to be satisfied in particular by so-called diagonal S -matrices, but presumably also in other cases such as the O ( N )-invariant nonlinear σ -models.
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ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-017-2891-0