The Future of Quantum Theory of Angular Momentum

Abstract

THE QUANTUM THEORY OF ANGULAR MOMENTUM began with Bohr’s enunciation of the rules for the quantization of orbital angular momentum in 1913, and the refinement of these rules by Sommerfeld [1] and Lande [2] within the framework of the old quantum theory. A basic result for angular momentum in modern quantum theory, which we call The First Fundamental Result, was given in the third foundational paper in 1926 by Born, Heisenberg, and Jordan [3], who not only gave the basic commutation relations for the components of the total angular momentum J, but all finite-dimensional Hermitian matrix representations of these components. Dirac [4] simultaneously deduced these basic commutation relations using his algebraic approach to quantum mechanics, and later gave a marvelously brief derivation of their matrix representations in his book [5]. Further developments, including the famous Pauli matrices and results relating to angular momentum selection rules for transitions in atomic systems, are given in the papers by Heisenberg and Jordan [6], Pauli [7], and Guttinger and Pauli [8]. These works, and the books by Born and Jordan [9] and Condon and Shortley [10], fixed the framework for much of the developments in angular momentum theory, which was hardly distinguishable from the general quantum theory in the context of which it was developed for the purpose of giving a consistent description of the spectra of atoms. Little emphasis was given to the universal and distinctive role of symmetry.