Non-commutative Solitons in Finite Quantum Mechanics

Abstract

We construct the unitary evolution operators that realize the quantization of linear maps of SL(2,R) over phase spaces of arbitrary integer discretization N and show the non-trivial dependence on the arithmetic nature of N. We discuss the corresponding uncertainty principle and construct the corresponding coherent states, that may be interpreted as non-commutative solitons.

Comments: 3 pages LaTeX. Uses espcrc2.sty and amssymb.sty. Contribution to Lattice 2002(theoretical)