Abstract
The generalized uncertainty principle (GUP) has brought the idea of the existence of a minimum measurable length in quantum physics. Depending on this GUP, the nonrelativistic Hamiltonian at the Planck scale is modified. In this paper, we construct the kernel for this GUP-corrected Hamiltonian for a free particle by applying the Hamiltonian path integral approach and checking 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.
- Received 2 July 2012
DOI:https://doi.org/10.1103/PhysRevD.86.085004
© 2012 American Physical Society