Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 100, 39 pages      arXiv:1602.04696

Bound State Operators and Wedge-Locality in Integrable Quantum Field Theories

Yoh Tanimoto ab
a) Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba Meguro-ku Tokyo 153-8914, Japan
b) Institut für Theoretische Physik, Göttingen University, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany

Received February 19, 2016, in final form October 10, 2016; Published online October 19, 2016

We consider scalar two-dimensional quantum field theories with a factorizing $S$-matrix which has poles in the physical strip. In our previous work, we introduced the bound state operators and constructed candidate operators for observables in wedges. Under some additional assumptions on the $S$-matrix, we show that, in order to obtain their strong commutativity, it is enough to prove the essential self-adjointness of the sum of the left and right bound state operators. This essential self-adjointness is shown up to the two-particle component.

Key words: Haag-Kastler net; integrable models; wedge; von Neumann algebras; Hardy space; self-adjointness.

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