A Topological Study of Induced Representation

TL;DR

This paper explores the topological aspects of Wigner's induced representation technique, analyzing gauge structures and applying the findings to quantum mechanics on a sphere with a formulated path integral.

Contribution

It provides a topological analysis of induced representations, constructs explicit gauge fields, and applies these results to quantum mechanics on a spherical manifold.

Findings

Explicit form of gauge fields in induced representations

Topological insights into gauge structures

Path integral formulation for quantum mechanics on a sphere

Abstract

From the point of view of topology we study the induced representation technique which E. Wigner proposed in 1939. We comment on the gauge structure in the induced representation technique and construc the explicit form of the gauge fields. The topological results ofour study are applied to quantum mechanics on a d-dimensional sphere and its path integral is formulated.