Massive $4d$ particle with torsion and conformal mechanics

TL;DR

This paper explores how coupling torsion to a massive spinless particle in 4D space-time results in a system with extended gauge invariance and a discrete mass spectrum described by conformal mechanics.

Contribution

It demonstrates that torsion coupling preserves spinless nature while inducing a nontrivial mass spectrum governed by conformal mechanics.

Findings

The system remains spinless despite torsion coupling.

Torsion induces a nontrivial mass spectrum.

Discrete mass spectra are achievable with specific parameters.

Abstract

The consequences of coupling of the torsion (highest curvature) term to the Lagrangian of a massive spinless particle in four-dimensional space-time are studied. It is shown that the modified system remains spinless and possesses extended gauge invariance. Though the torsion term does not generate spin, it provides the system with a nontrivial mass spectrum, described by one-dimensional conformal mechanics. Under an appropriate choise of characteristic constants the system has solutions with a discrete mass spectrum.