Bianchi type-V spinning particle on 2-sphere

TL;DR

This paper constructs an integrable model of a spinning particle on a 2-sphere using Bianchi type-V algebra, exploring generalizations and connections to black hole backgrounds and superconformal mechanics.

Contribution

It introduces a novel integrable spinning particle model on a 2-sphere with Bianchi type-V algebra and explores its generalizations and physical implications.

Findings

Constructed an integrable spinning particle model on 2-sphere.

Extended the model to include scalar potentials and external fields.

Linked the model to relativistic particles near black hole horizons.

Abstract

Integrable spinning extension of a free particle on 2-sphere is constructed in which spin degrees of freedom are represented by a 3-vector obeying the Bianchi type-V algebra. Generalizations involving a scalar potential giving rise to two quadratic constants of the motion, or external field of the Dirac monopole, or the motion on the group manifold of SU(2) are built. A link to the model of a relativistic spinning particle propagating on the near horizon 7d Myers-Perry black hole background is considered. Implications of the construction in this work for the D(2,1;a) superconformal mechanics are discussed.