Quantum Mechanical Embedding of Spinning Particle and Induced Spin-connection

TL;DR

This paper presents a quantum mechanical embedding method for spinning particles, deriving gauge fields as spin connections, and connects to previous models on the $S^2$ manifold, enhancing understanding of spin geometry.

Contribution

It introduces a novel quantum embedding approach for spinning particles that naturally yields gauge fields as spin connections, extending prior models to more general submanifolds.

Findings

Gauge field as spin connection derived from Schrödinger equation

Reduction to known models on $S^2$ in $R^3$

Provides a geometric framework for spinning particles

Abstract

This paper introduces the way of the embedding of spinning particle quantum mechanically. Schr\"odinger equation on its submanifold obtains the gauge field as spin connection, and it reduces to the ones obtained by Ohnuki and Kitakado when we consider $S^2$ in $R^3$. PACS numbers: 03.65