Geometry of physical dispersion relations

Understand

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.