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.
Highlights
In recent years, we have seen many interesting developments in constructing models of quantum field theory (QFT) in the operator-algebraic approach [25]
Borchers triples for analytic S-matrices For the class of two-particle scattering functions S(θ ) which are analytic in the physical strip θ ∈ R + i(0, π ), local observables associated with wedge-regions, say with the standard left wedge WL, can be constructed by following an argument due to Schroer [39] and Lechner [27]
Our aim was to extend Lechner’s construction of two-dimensional models of quantum field theory with a factorizing scattering matrix to models with bound states, which are associated with poles of the S-matrix in the physical strip
Summary
We have seen many interesting developments in constructing models of quantum field theory (QFT) in the operator-algebraic approach [25]. Solutions of the form factor equations should represent the matrix components of local operators, and their commutators should vanish when they are spacelike separated Such a formal proof has been given first by Smirnov for S-matrices without poles [41]. The general form of the S-matrix that we obtain is essentially given by a certain subclass of S-matrices known from [28] multiplied with a universal model independent factor which has poles in the physical strip. 3 we summarize the properties of scalar S-matrices with poles in the physical strip in the models under investigation, and we construct the wedge-local fields φ, φ. Appendix C comments on the problem of finding suitable self-adjoint extensions of the field φ
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
