Wedge-Local Fields in Integrable Models with Bound States

Abstract

Abstract:Recently, large families of two-dimensional quantum field theories with factorizing S-matrices have been constructed by the operator-algebraic methods, by first showing the existence of observables localized in wedge-shaped regions. However, these constructions have been limited to the class of S-matrices whose components are analytic in rapidity in the physical strip. In this work, we construct candidates for observables in wedges for scalar factorizing S-matrices with poles in the physical strip and show that they weakly commute on a certain domain. We discuss some technical issues concerning further developments, especially the self-adjointness of the candidate operators here and strong commutativity between them.

Towards an Explicit Construction of Local Observables in Integrable Quantum Field Theories

“…However, on the side of the operator algebraic approach, the wedge-local fields can no longer have the simple form (2.14). Work towards a construction of wedge-local fields and of local algebras A(O) in this case has recently been carried out by one of the authors together with Y. Tanimoto [38,39,40]. This gives hope that our present methods, with a suitably modified version of Theorem 2.2, can be applied to models with bound states as well.…”

Strengthened Reeh–Schlieder Property and Scattering in Quantum Field Theories Without Mass Gaps

“…19 Preliminary computations suggest that Ω ∈ D(T 1+ǫ ) could be fulfilled in certain 1+1-dimensional integrable models with non-temperate polarization free generators G [CT15] [Yoh Tanimoto, private communications]. A definite assessment requires the construction of a Borchers triple for these models, which has not yet been completed at the time of writing of this work.…”

Inverse Scattering and Local Observable Algebras in Integrable Quantum Field Theories

“…However, for a large class of non-scalar S-matrices a solution of the inverse scattering problem is obtained. We expect that (slight variations of) our methods will also apply to models with bound states, as they are currently being analyzed by Cadamuro and Tanimoto [20]. This paper is based on the PhD thesis of one of us [2].…”

“…The present paper follows an alternative inverse scattering approach to the construction of integrable quantum field theories, see [49,50,35,38] for the initial papers in this program, [8,14,42,20,56] for more recent developments, and [40, Ch. 10] for a review.…”

“…Two possible extensions are to consider only meromorphic (instead of analytic) S-matrices, with the poles of S related to the bound states of the theory, or infinite-dimensional S, as is necessary for describing situations in which the gauge group is no longer compact. We refer to [20,56] and [28] for new developments in these two directions. It should be noted, however, that our setup already allows for a huge family of models, including the O(N ) σ-models as particular examples.…”