The Principle of Solidarity: Geometrical Description of Interactions

TL;DR

This paper explores a geometric approach to modeling interactions by deforming Minkowski spacetime metrics based on energy dependence, enabling analysis of Lorentz invariance violations within a generalized framework.

Contribution

It introduces a formalism called Deformed Special Relativity that geometrizes interactions through energy-dependent metric deformations, extending traditional relativity.

Findings

Allows modeling of Lorentz invariance breakdowns

Provides a geometric framework for energy-dependent interactions

Enables recovery of Lorentz invariance in a generalized sense

Abstract

We discuss the possibility of geometrizing interactions by exploiting the "principle of solidarity" between space-time and the physical phenomena occurring in it (formulated by the Italian matematician B. Finzi in 1955). This is accomplished by means of a deformation of the Minkowski metric, implemented by assuming that the metric coefficients depend on the energy of the process considered. Such a formalism ("Deformed Special Relativity") allows one, among the others, to deal with the breakdown of Lorentz invariance and to recover it in a generalized sense.