Geometry of physical dispersion relations

TL;DR

This paper derives algebraic conditions for physical dispersion relations from fundamental physical principles, restricting modifications of standard relativistic relations and ruling out certain deformed theories.

Contribution

It establishes simple algebraic criteria for dispersion relations based on physical requirements, limiting the scope of permissible modifications.

Findings

Standard relativistic dispersion relations satisfy the derived conditions.

Certain deformations like Gambini-Pullin and Myers-Pospelov are incompatible with these conditions.

The conditions ensure predictive matter dynamics and observer-independent energy positivity.

Abstract

To serve as a dispersion relation, a cotangent bundle function must satisfy three simple algebraic properties. These conditions are derived from the inescapable physical requirements to have predictive matter field dynamics and an observer-independent notion of positive energy. Possible modifications of the standard relativistic dispersion relation are thereby severely restricted. For instance, the dispersion relations associated with popular deformations of Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible.