Diffraction in Time of Polymer Particles

TL;DR

This paper investigates the quantum dynamics of polymer particles, showing convergence to standard quantum results at low energy and revealing unique high-energy behaviors and the absence of diffraction in time phenomena.

Contribution

It introduces a polymer quantization scheme for particle dynamics, highlighting new high-energy effects and the impact on diffraction phenomena compared to standard quantum mechanics.

Findings

Polymer distribution converges to standard quantum results at low energy.

High-energy polymer behavior dominates at short distances and times.

Particles satisfying the polymer wave equation do not show diffraction in time.

Abstract

We study the quantum dynamics of a suddenly released beam of particles using a background independent (polymer) quantization scheme. We show that, in the first order of approximation, the low-energy polymer distribution converges to the standard quantum-mechanical result in a clear fashion, but also arises an additional small polymer correction term. We find that the high-energy polymer behaviour becomes predominant at short distances and short times. Numerical results are also presented. We find that particles whose wave functions satisfy the polymer wave equation do not exhibit the diffraction in time phenomena. The implementation of a lower bound to the possible resolution of times into the time-energy Heisenberg uncertainty relation is briefly discussed.