Spin Quantization and the Relativistically Spinning Sphere

John French

D. ter Haar

Yu. M. Shirokov

Zhong-Shuai 中帅 Zhang 张, Shi-Fa Xiao, Damao Xun +1 more

For a non-relativistic particle that freely moves on a curved surface, the fundamental commutation relations between positions and momenta are insufficient to uniquely determine the operator form of the momenta. With introduction of more commutation relations between positions and Hamiltonian and those between momenta and Hamiltonian, our recent sequential studies imply that the Cartesian system of coordinates is physically preferable, consistent with Dirac' observation. In present paper, we study quantization problem of the motion constrained on the two-dimensional sphere and develop a discriminant that can be used to show how the quantization within the intrinsic geometry is improper. Two kinds of parameterization of the spherical surface are explicitly invoked to investigate the quantization problem within the intrinsic geometry.

Hiroshi Enatsu

Giuseppe Bimonte, Giovanni Sparano

Topological considerations, in apparent disagreement with operatorial ones, seem to suggest that only integer and half-integer spins are possible on a sphere. In this letter we show that fractional spin is indeed possible on a sphere, but only by breaking the rotational invariance. As we will show in a subsequent paper, this is an example of the fact that the quantizations individuated by the covering space are those that preserve the continuous classical symmetries.