Diffraction in Time of Polymer Particles

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.