The authors assume that there is a minimal area, i.e., that the
usual (i.e., Heisenberg's) commutation relations between the
coordinate and momentum happen to be complemented by a nontrivial
commutator between x and y coordinates (in two dimensions). The two
illustrative examples are then constructed, i.e., the formulae for
commutators between creation and annihilation operators leading to
the two respective awkward (so called deformed) oscillator algebras
are deduced. In the opposite direction the authors start from a
``nice" (i.e., Fock-space-construction admitting) deformed
oscillator algebra and deduce the resulting cumbersome
generalization of the commutation relations between the coordinate
and momentum. A discussion of some special cases is added.


MR2726711 Fring, Andreas; Gouba, Laure; Bagchi, Bijan Minimal areas
from $q$-deformed oscillator algebras. J. Phys. A 43 (2010), no. 42,
425202, 13 pp. 81R50