The Geometry of a $q$-Deformed Phase Space

Details The Geometry of a $q$-Deformed Phase Space The Geometry of a $q$-Deformed Phase Space

1998-07-22

arxiv.org/abs/math/9807123v2

Eur.J.Phys. C8 (1999) 533-546

Mathematics

Quantum Algebra

latex file, 26 pp, a typing error corrected

Scientific paper

The geometry of the $q$-deformed line is studied. A real differential calculus is introduced and the associated algebra of forms represented on a Hilbert space. It is found that there is a natural metric with an associated linear connection which is of zero curvature. The metric, which is formally defined in terms of differential forms, is in this simple case identifiable as an observable.

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