q-Derivatives, quantization methods and q-algebras

Details q-Derivatives, quantization methods and q-algebras q-Derivatives, quantization methods and q-algebras

Dec 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998aipc..453..146t&link_type=abstract

Particles, fields and gravitation. AIP Conference Proceedings, Volume 453, pp. 146-154 (1998).

Physics

Theory Of Quantized Fields, Field Theory, Algebraic Methods

Scientific paper

Using the example of Borel quantization on S1, we discuss the relation between quantization methods and q-algebras. In particular, it is shown that a q-deformation of the Witt algebra with generators labeled by Z is realized by q-difference operators. This leads to a discrete quantum mechanics. Because of Z, the discretization is equidistant. As an approach to a non-equidistant discretization of quantum mechanics one can change the Witt algebra using not the number field Z as labels but a quadratic extension of Z characterized by an irrational number τ. This extension is denoted as quasi-crystal Lie algebra, because this is a relation to one-dimensional quasicrystals. The q-deformation of this quasicrystal Lie algebra is discussed. It is pointed out that quasicrystal Lie algebras can be considered also as a ``deformed'' Witt algebra with a ``deformation'' of the labeling number field. Their application to the theory is discussed.

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