A Generalized Uncertainty Principle from a Mediating Field

• URL: http://arxiv.org/abs/2003.06964v2
• Date: Thu, 23 Apr 2020 09:08:02 GMT
• Title: A Generalized Uncertainty Principle from a Mediating Field
• Abstract summary: The Lagrange multiplier is found to obey a relativistic diffusion equation transforming the internal coordinates of the scalar field. It is conjectured that infrared and ultraviolet divergences are naturally removed in studying the infinite-order partial differential equation. It is suggested that higher-order contributions of the associated commutation relations are reminiscent of a self-interaction not present in the current quantum theory.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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