Fermion Quasi-Spherical Harmonics

Details Fermion Quasi-Spherical Harmonics Fermion Quasi-Spherical Harmonics

1998-10-02

arxiv.org/abs/math-ph/9810001v1

Physics

Mathematical Physics

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

Scientific paper

10.1088/0305-4470/32/5/011

Spherical Harmonics, $Y_\ell^m(\theta,\phi)$, 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 $\phi$. 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 $\phi$, 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.

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