Effective field theory from Relativistic Generalized Uncertainty

TL;DR

This paper develops a Lorentz-invariant relativistic generalized uncertainty principle, formulates compatible quantum field theories, and derives quantum gravity corrections to scattering processes, improving bounds on quantum gravity scales.

Contribution

It introduces a Lorentz invariant formulation of the GUP, constructs consistent quantum field theories, and computes quantum gravity corrections to scattering cross-sections.

Findings

Derived Lorentz invariant minimal length consistent with GUP

Constructed Lagrangians for scalar, spinor, and gauge fields

Calculated quantum gravity corrections to lepton scattering

Abstract

Theories of Quantum Gravity predict a minimum measurable length and a corresponding modification of the Heisenberg Uncertainty Principle to the so-called Generalized Uncertainty Principle (GUP). However, this modification is usually formulated in non-relativistic language, making it unclear whether the minimum length is Lorentz invariant. We have formulated a Relativistic Generalized Uncertainty Principle, resulting in a Lorentz invariant minimum measurable length and the resolution of the composition law problem. This proved to be an important step in the formulation of Quantum Field Theory with minimum length. We derived the Lagrangians consistent with the existence of minimal length and describing the behaviour of scalar, spinor, and U(1) gauge fields. We calculated the Feynman rules (propagators and vertices) associated with these Lagrangians. Furthermore, we calculated the Quantum Gravity corrected scattering cross-sections for a lepton-lepton scattering. Finally, we compared our results with current experiments, which allowed us to improve the bounds on the scale at which quantum gravity phenomena will become relevant.