Quasi-Continuous Symmetries of Non-Lie Type

Abstract

We introduce a smooth mapping of some discrete space-time symmetries into quasi-continuous ones. Such transformations are related with q-deformations of the dilations of the Euclidean space and with the non-commutative space. We work out two examples of Hamiltonian invariance under such symmetries. The Schrodinger equation for a free particle is investigated in such a non-commutative plane and a connection with anyonic statistics is found.

Comments: 18 pages, LateX, 3 figures, Submitted Found. Phys., PACS: 03.65.Fd, 11.30.Er