A short study of a string on a plane: the energy and the effective mass

TL;DR

This paper explores a special class of finite strings on a plane, defining their energy and effective mass within a new phase space framework, revealing strong classical correlations and extending Galilei symmetry concepts.

Contribution

It introduces a novel phase space for a non-relativistic string, defines its energy via group invariants, and proposes a new concept of effective mass for such systems.

Findings

Defined energy using Casimir functions of the extended Galilei group

Introduced the concept of effective mass for the string system

Discussed classical correlations between degrees of freedom

Abstract

We investigate the new special class of the finite string on a plane, after the reduction from the relativistic $4D$ case. The suggested special form of the phase space allows to define the extended Galilei group as a group of the space - time symmetry for the considered system. The definition of the energy for the studied non-relativistic string through the Cazimir function of this group is suggested. The concept of the effective mass for the investigated dynamical system is introduced. The appearance of strong correlations between the degrees of freedom even on the classical level is discussed.