Group-Theoretical Derivation of Angular Momentum Eigenvalues in Spaces of Arbitrary Dimensions

TL;DR

This paper derives the spectrum of angular momentum in any number of dimensions using group theory, specifically the Lie algebra of the noncompact group O(2,1), providing a unified algebraic approach.

Contribution

It introduces a group-theoretical method to determine angular momentum eigenvalues in arbitrary dimensions, expanding beyond traditional approaches.

Findings

Derived the spectrum of angular momentum in arbitrary dimensions.

Applied Lie algebra of O(2,1) to obtain eigenvalues.

Provided a unified algebraic framework for angular momentum analysis.

Abstract

The spectrum of the square of the angular momentum in arbitrary dimensions is derived using only group theoretical techniques. This is accomplished by application of the Lie algebra of the noncompact group O(2,1).