Mass, Impetus and Force by Symplectic Realizations of the Static Group

TL;DR

This paper uses symplectic realizations of the Static group to model a massive particle with invariant force and impetus, characterizing its physical quantities and Hamiltonian structure.

Contribution

It introduces a novel symplectic realization approach to describe particles with invariant force and impetus within the Static group framework.

Findings

Maximal G-elementary system is a massive particle with invariant force and impetus.

System characterized by mass, boost, acceleration, and internal energy.

Hamiltonian includes potential energy and impetus contribution.

Abstract

We show by symplectic realizations of the one dimensional Static group $G$ that the maximal $G$-elementary system is a a massive particle under an invariant force $f$ participating in the linear momentum and an invariant impetus $I$ participating in the change of position. Moreover the system is characterized by four physical quantities : a mass $m$, a boost $u=\frac{I}{m}$, an acceleration $a=\frac{f}{m}$ and an internal energy $U$. The hamiltonian of the system is a sum of the potential energy $V=-fq$ and a contribution $pu$ of the impetus.