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 $\mathit{SO}(3)_q$ are studied.
 Publication:

arXiv eprints
 Pub Date:
 March 2019
 arXiv:
 arXiv:1903.00318
 Bibcode:
 2019arXiv190300318O
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Quantum Physics