Quantum fields for unitary representations of Thompson's groups F and T

Abstract

We describe how to define observables analogous to quantum fields for the semicontinuous limit recently introduced by Jones in the study of unitary representations of Thompson's groups $F$ and $T$. We find that, in terms of correlation functions of these fields, one can deduce quantities resembling the conformal data, i.e., primary fields, scaling dimensions, and the operator product expansion. Examples coming from quantum spin systems and anyon chains built on the trivalent category $SO(3{)}_q$ are studied.

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Cited by in corpus (5)

• Scaling limits of lattice quantum fields by wavelets
• Conformal field theory from lattice fermions
• Canonical quantization of 1+1-dimensional Yang-Mills theory: An operator-algebraic approach
• Operator-algebraic renormalization and wavelets
• On Jones' connections between subfactors, conformal field theory, Thompson's groups and knots