New insights in particle dynamics from group cohomology

TL;DR

This paper explores particle dynamics using group cohomology, revealing how physical constants emerge as group extension parameters and proposing a new force from gravity-electromagnetism mixing.

Contribution

It introduces a cohomological framework for particle dynamics that uncovers new insights into fundamental interactions and potential testable predictions.

Findings

Physical constants as group extension parameters

Derivation of a non-relativistic limit via Inonu-Wigner contraction

Proposal of a new force from gravity-electromagnetism mixing

Abstract

The dynamics of a particle moving in background electromagnetic and gravitational fields is revisited from a Lie group cohomological perspective. Physical constants characterising the particle appear as central extension parameters of a group which is obtained from a centrally extended kinematical group (Poincare or Galilei) by making local some subgroup. The corresponding dynamics is generated by a vector field inside the kernel of a presymplectic form which is derived from the canonical left-invariant one-form on the extended group. A non-relativistic limit is derived from the geodesic motion via an Inonu-Wigner contraction. A deeper analysis of the cohomological structure reveals the possibility of a new force associated with a non-trivial mixing of gravity and electromagnetism leading to in principle testable predictions.