Fermion Quasi-Spherical Harmonics

Abstract

Spherical Harmonics, $Y_{\ell }^m(\theta ,\varphi )$, are derived and presented (in a Table) for half-odd-integer values of $\ell$ and $m$. These functions are eigenfunctions of $L^2$ and $L_z$ written as differential operators in the spherical-polar angles, $\theta$ and $\varphi$. The Fermion Spherical Harmonics are a new, scalar and angular-coordinate-dependent representation of fermion spin angular momentum. They have $4\pi$ symmetry in the angle $\varphi$, and hence are not single-valued functions on the Euclidean unit sphere; they are double-valued functions on the sphere, or alternatively are interpreted as having a double-sphere as their domain.

16 pages, 2 Tables. Submitted to J.Phys.A

Cited by in corpus (6)

• A Bilocal Model for the Relativistic Spinning Particle
• Rigid Particle and its Spin Revisited
• Groups, Jacobi functions and rigged Hilbert spaces
• Legendre Functions of Fractional Degree: Transformations and Evaluations
• On the non-Abelian monopoles on the background of spaces with constant curvature
• Spin 1 particle in the magnetic monopole potential, nonrelativistic approximation. Minkowski and Lobachevski spaces