A Discrete Time Presentation of Quantum Dynamics

Abstract

Inspired by the discrete evolution implied by the recent work on loop quantum cosmology, we obtain a discrete time description of usual quantum mechanics viewing it as a constrained system. This description, obtained without any approximation or explicit discretization, mimics features of the discrete time evolution of loop quantum cosmology. We discuss the continuum limit, physical inner product and matrix elements of physical observables to bring out various issues regarding viability of a discrete evolution. We also point out how a continuous time could emerge without appealing to any continuum limit.

20 pages, RevTex, no figures. Additional Clarifications added. Version accepted for publication in Class. Quant. Grav