Generalized Hamilton spaces: new developments and applications

TL;DR

This paper advances the theory of generalized Hamilton spaces by deriving key geometrical structures from metrics, analyzing their properties, and exploring applications in quantum gravity and non-commutative spacetimes.

Contribution

It introduces new developments in cotangent bundle geometries, focusing on deriving connections from metrics and examining their properties and applications.

Findings

Properties of autoparallel Hamiltonians demonstrated

Spacetime and momentum isometries analyzed

Potential applications in quantum gravity discussed

Abstract

In this work, we make new developments in generic cotangent bundle geometries, depending on all phase-space variables. In particular, we will focus on the so-called generalized Hamilton spaces, discussing how the main ingredients of this geometrical framework, such as the Hamiltonian and the nonlinear and affine connections, can be derived from a given metric. Several properties of this kind of spaces are demonstrated for autoparallel Hamiltonians. Moreover, we study the spacetime and momentum isometries of the metric. Finally, we discuss the possible applications of cotangent bundle geometries in quantum gravity, such as the construction of deformed relativistic kinematics and non-commutative spacetimes.