Abstract
We consider the construction of integrable quantum field theories in the operator-algebraic approach, which is based on quantum fields localized in infinitely extended wedge regions. This approach has been successful for the construction of a class of models with scalar S-matrices and without bound states. In extension of these results, we apply similar methods to S-matrices with poles in the physical strip (“bound states”). Specifically, we consider a deformed version of the Sine-Gordon model, containing only breathers. We exhibit wedge-local fields in this model, which differ from those in non-bound state models by an additive term, the so called “bound state operator”.
Highlights
The construction of interacting quantum field theories is a difficult problem in Mathematical Physics
There is a class of quantum field theories that can be constructed with techniques which avoid perturbative expansions: the quantum integrable models
We report on progress towards a construction of a deformed version of the SineGordon model, which contains only “breather” particles (Sec. 3)
Summary
The construction of interacting quantum field theories is a difficult problem in Mathematical Physics. They are constructed as an inverse scattering problem: Given a function S as a mathematical input, one constructs the corresponding QFT having this two-particle scattering function The interaction of these models is simple enough for certain methods familiar from free field theory to be carried over to the interacting situation. They can be regarded as simplified analogues of four-dimensional nonabelian gauge theories, inasmuch as they share crucial features with them, including renormalizability, asymptotic freedom, and the existence of instanton solutions In this sense, integrable systems provide a “landscape” of possible interactions, where one may hope to test techniques that can be adapted to, or inspire methods for, systems in higher dimensions, and where one may obtain insight into the structure of local QFTs with a less simple S-matrix. Processes (ss) −→ bk (sbk) −→ s (sbk) −→ s (bkbl) −→ bk+l (bk+lbk) −→ bl rapidities of particles θ(bsks)
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