A Deformation of Quantum Dynamics through the Phase Space Path Integral

TL;DR

This paper explores a modified quantum dynamics framework using a regularised phase space path integral, introducing a fundamental time scale with potential implications for quantum field theory and gravity.

Contribution

It presents a novel deformation of quantum dynamics via a phase space path integral with a new fundamental time scale, motivated by noncommutative geometry.

Findings

Achieved intriguing results in the harmonic oscillator model.

Suggested potential extensions to quantum field theory and gravity.

Proposed a new perspective on time in quantum mechanics.

Abstract

Using a regularised construction of the phase space path integral due to Ingrid Daubechies and John Klauder which involves a time scale ultimately taken to vanish, and motivated by the general programme towards a noncommutative space(time) geometry, physical consequences of assuming this time parameter to provide rather a new fundamental time scale are explored in the context of the one dimensional harmonic oscillator. Some tantalising results are achieved, which raise intriguing prospects when extrapolated to the quantum field theory and gravitational contexts.