The induced representation of the isometry group of the Euclidean Taub-NUT space and new spherical harmonics

TL;DR

This paper explores the symmetry properties of the Euclidean Taub-NUT space, revealing how its isometry group induces a novel form of spherical harmonics and spinors through combined representations.

Contribution

It introduces a new induced representation of the isometry group that explains the structure of spherical harmonics and spinors on the Euclidean Taub-NUT space.

Findings

Derived the transformation law of the fourth coordinate under rotations.

Identified a new type of spherical harmonics and spinors.

Explained the special form of the angular momentum operator.

Abstract

It is shown that the SO(3) isometries of the Euclidean Taub-NUT space combine a linear three-dimensional representation with one induced by a SO(2) subgroup, giving the transformation law of the fourth coordinate under rotations. This explains the special form of the angular momentum operator on this manifold which leads to a new type of spherical harmonics and spinors.