Scaling limits of integrable quantum field theories and non-local chiral models

Scotford, Charley 2023. Scaling limits of integrable quantum field theories and non-local chiral models. PhD Thesis, Cardiff University. Item availability restricted.

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Abstract

In this thesis, short distance scaling limits of integrable quantum field theoretic models are explored. We consider an integrable model as a representation of two abstract Zamolodchikov-Faddeev algebras on an S-symmetric Fock space which are related in a specific manner. The defining datum of such an algebra is an R-matrix, namely an involutive, unitary solution of the Yang-Baxter equation with spectral parameters. We show how such R-matrices S (on the tensor product of Hilbert spaces HaH) and R (on KaK) can be combined into a box-sum S t R and how this operation is refected on the level of the Fock spaces FS(H);FR(K);FStR(H`K). The construction of chiral models as the short-distance scaling limit of such integrable models is outlined and the implications of such equivalences are discussed in this one-dimensional setting. In particular, we investigate the local observable content of the resulting chiral models. It is shown how the R-matrix relates to an algebra of observables localised at infinity, and how this algebra encodes the local observable content. In a specific example, we show how a deformation procedure produces strongly non-local models without strictly local observables.

Item Type:	Thesis (PhD)
Date Type:	Completion
Status:	Unpublished
Schools:	Mathematics
Date of First Compliant Deposit:	21 June 2023
Last Modified:	06 Jan 2024 04:24
URI:	https://orca.cardiff.ac.uk/id/eprint/160479

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