A Generalized Uncertainty Principle from a Mediating Field
Abstract
A generalized uncertainty principle is obtained from a conformally transformed action containing a scalar field and a unique constraint. The constraint's Lagrange multiplier is found to obey a relativistic diffusion equation transforming the internal coordinates of the scalar field, via the shift theorem. For an approximately conserved Noether current, the coupled wave- and diffusion-like equations are merged into an infinite-order partial differential equation (PDE). It is conjectured that infrared and ultraviolet divergences are naturally removed in studying the infinite-order PDE's corresponding propagator. It is further suggested that higher-order contributions of the associated commutation relations are reminiscent of a self-interaction not present in the current quantum theory.
Cite
@article{arxiv.2003.06964,
title = {A Generalized Uncertainty Principle from a Mediating Field},
author = {Dor Gabay},
journal= {arXiv preprint arXiv:2003.06964},
year = {2020}
}