Path Integral for non-relativistic Generalized Uncertainty Principle corrected Hamiltonian

TL;DR

This paper constructs a path integral kernel for a GUP-modified non-relativistic Hamiltonian, revealing a maximum momentum bound consistent with GUP predictions, and thoroughly checks its validity.

Contribution

It introduces a path integral formulation for GUP-corrected Hamiltonians and explores the resulting momentum bounds, advancing understanding of quantum mechanics at the Planck scale.

Findings

Kernel construction for GUP-corrected Hamiltonian

Identification of a maximum momentum bound

Validation of the kernel's probabilistic interpretation

Abstract

Generalized Uncertainty Principle (GUP) has brought the idea of existence of minimum measurable length in Quantum physics. Depending on this GUP, non-relativistic Hamiltonian at the Planck scale is modified. In this article, we construct the kernel for this GUP corrected Hamiltonian for free particle by applying the Hamiltonian path integral approach and check the validity conditions for this kernel thoroughly. Interestingly, the probabilistic interpretation of this kernel induces a momentum upper bound in the theory which is comparable with GUP induced maximum momentum uncertainty.