Unitary Evolution on a Discrete Phase Space
High Energy Physics - Lattice
2007-05-23 v1
Abstract
We construct unitary evolution operators on a phase space with power of two discretization. These operators realize the metaplectic representation of the modular group SL(2,Z_{2^n}). It acts in a natural way on the coordinates of the non-commutative 2-torus, T_{2^n}^2$ and thus is relevant for non-commutative field theories as well as theories of quantum space-time. The class of operators may also be useful for the efficient realization of new quantum algorithms.
Keywords
Cite
@article{arxiv.hep-lat/0510043,
title = {Unitary Evolution on a Discrete Phase Space},
author = {E. G. Floratos and S. Nicolis},
journal= {arXiv preprint arXiv:hep-lat/0510043},
year = {2007}
}
Comments
5 pages, contribution to Lattice 2005 (theoretical developments)