Rainbow metric formalism and Relative Locality

TL;DR

This paper explores the Rainbow metric formalism within the Relative Locality framework, demonstrating its equivalence to the Hamiltonian formalization and discussing ongoing research in this area.

Contribution

It establishes the equivalence between Rainbow metrics and Hamiltonian formalization in Relative Locality, advancing the theoretical understanding of momentum-dependent geometries.

Findings

Rainbow metric formalism is equivalent to Hamiltonian formalization.

The work is based on ongoing research with collaborators.

The formalism provides insights into momentum-dependent spacetime structures.

Abstract

This proceeding is based on a talk prepared for the XIII Marcell Grossmann meeting. We summarise some results of work in progress in collaboration with Giovanni Amelino-Camelia about momentum dependent (Rainbow) metrics in a Relative Locality framework and we show that this formalism is equivalent to the Hamiltonian formalization of Relative Locality obtained in arXiv:1102.4637.