Abstract
This short report sketches new results in the application of the ‘quantum groups’1,2 in 1 + 1 dimensions. They concern two aspects:- (i) generation of new quantum (and classical) integrable models in 1 + 1 — we report solution of a new “q-boson” lattice model which is quantum integrable; (ii) the very physical question of whether there are experimentally realisable systems where quantisation by a quantum group (“q-quantisation”) could be distinguished from ordinary canonical quantisation. We suggest quantum optical experiments involving Rydberg atoms in microwave cavities (cavity q.e.d.3,4) where our predictions are different in the two cases. In contrast we show that for the integrable quantum field theories predictions are identical in the two cases. Thus ordinary q.e.d. based on the quantised Maxwell equations is apparently unchanged by q-quantisation. We show that the new “q-boson” lattice model exemplifies similar features.
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