Asymptotic Completeness in a Class of Massless Relativistic Quantum Field Theories

Abstract

This paper presents the first examples of massless relativistic quantum field theories which are interacting and asymptotically complete. These two-dimensional theories are obtained by an application of a deformation procedure, introduced recently by Grosse and Lechner, to chiral conformal quantum field theories. The resulting models may not be strictly local, but they contain observables localized in spacelike wedges. It is shown that the scattering theory for waves in two dimensions, due to Buchholz, is still valid under these weaker assumptions. The concepts of interaction and asymptotic completeness, provided by this theory, are adopted in the present investigation.

Infraparticles with Superselected Direction of Motion in Two-Dimensional Conformal Field Theory

“…In this subsection we show that any such regular chiral net has a complete particle interpretation in terms of non-interacting Wigner particles. These facts follow from our results in [25], but the argument below is more direct.…”

“…(We demonstrated these facts already in [25] in a different context.) To conclude this subsection, we introduce some other useful concepts which are needed in Theorem 2.11 below: Let us choose some closed subspaces K ± ⊂ H ± , invariant under the action of U , and denote by K + out × K − the linear span of the respective scattering states.…”

“…For this purpose we consider a particle weight ψ, whose GNS representation is of type I with atomic center and acts on a separable Hilbert space H π ψ . Making use of formula (2.24) and identifying unitarily each π α,e , acting on W −1 (H α ⊗ Ce), with π α := π α,e 0 acting on K α := W −1 (H α ⊗ Ce 0 ) for some chosen e 0 ∈ B α , we obtain 25) where the r.h.s. acts on α∈I {K α ⊗ K α }.…”

“…25) for any open, bounded interval I ⊂ R and any t ∈ R. We assume that W gives rise to a non-trivial representation of the group Z 2 , i.e. AdW = id and W 2 = I .…”

Deformations of Quantum Field Theories and Integrable Models

“…In the framework of Wightman field theories, this deformation manifests itself as a deformation of the tensor product of the testfunction algebra [GL08], and later on, the connection to Rieffel's strict deformation quantization [Rie92] was explored [BLS10]. By now, the warped convolution technique has also successfully been applied to the deformation of conformal field theories [DT10] and quantum field theories on curved spacetimes [DLM11].…”