An operator expansion for integrable quantum field theories

Abstract

A large class of quantum field theories on 1+1 dimensional Minkowski space, namely, certain integrable models, has recently been constructed rigorously by Lechner. However, the construction is very abstract and the concrete form of local observables in these models remains largely unknown. Aiming for more insight into their structure, we establish a series expansion for observables, similar but not identical to the well-known form factor expansion. This expansion will be the basis for a characterization and explicit construction of local observables, to be discussed elsewhere. Here, we establish the expansion independent of the localization aspect, and analyze its behavior under space-time symmetries. We also clarify relations with deformation methods in quantum field theory, specifically, with the warped convolution in the sense of Buchholz and Summers.

Wedge-Local Fields in Integrable Models with Bound States

“…It was shown in [11] that this expansion holds for every operator or quadratic form A in a certain regularity class and it is independent of the localization region of A. It is similar to the well-known form factor expansion, although it is not identical to it; for a pointlike field A, the definition of the coefficients f m,n (θ θ θ, η η η), there is an explicit expression in term of vacuum expectation values of A [11], and it was shown in [12] that if A is a general observable localized in a bounded region, then the f…”

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

“…3.1]. The symmetry representation U acts on Q ω by adjoint action, and correspondingly on the expansion coefficients f m,n [A]; we refer to [17,Sec. 3.3] for details.…”

Relativistic corrections to the Moyal-Weyl spacetime

“…an associative product, was used for the definition and hence the commutator has the standard properties. Furthermore, it is interesting to note that in [BC13], a similar commutator was given and dubbed the Q-commutator. It differs from our current definition only by an additional term, which is the commutative product of the two operators A, B ∈ C ∞ .…”