A Discrete Time Presentation of Quantum Dynamics

TL;DR

This paper presents a novel discrete time formulation of quantum mechanics inspired by loop quantum cosmology, exploring its properties, continuum limit, and potential emergence of continuous time without approximation.

Contribution

It introduces a discrete time description of quantum mechanics as a constrained system, inspired by loop quantum cosmology, without relying on approximation or explicit discretization.

Findings

Discrete time quantum dynamics mimics loop quantum cosmology features

Analysis of continuum limit and physical inner product

Discussion on emergence of continuous time from discrete formulation

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.