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

2019/03/01 by Tobias J. Osborne, Osborne, Tobias J., Deniz E. Stiegemann +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1903.00318

openalex publication_date 2019/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Continuum Limits of Quantum Lattice Systems

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