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CONSTRUCTION OF TWO-DIMENSIONAL QUANTUM FIELD MODELS THROUGH LONGO–WITTEN ENDOMORPHISMS

Part of: Scattering theory Quantum field theory; related classical field theories

Published online by Cambridge University Press:  10 April 2014

YOH TANIMOTO
YOH TANIMOTO*
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, Institut für Theoretische Physik, Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, [email protected]

Abstract

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We present a procedure for constructing families of local, massive and interacting Haag–Kastler nets on the two-dimensional spacetime through an operator-algebraic method. A proof of existence of local observables is given without relying on modular nuclearity. By a similar technique, another family of wedge-local nets is constructed using certain endomorphisms of conformal nets recently studied by Longo and Witten.

MSC classification

Secondary: 81T05: Axiomatic quantum field theory; operator algebras 81T40: Two-dimensional field theories, conformal field theories, etc. 81U99: None of the above, but in this section
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 2 , 01 July 2014 , e7
Creative Commons
Creative Common License - CCCreative Common License - BY
The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution licence .
Copyright
© The Author 2014

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