Generalized Uhlenbeck-Goudsmit hypothesis 'Magnetic' S^{a} and 'Electric' Z^{a} Spins

Abstract

In this paper, the connection between the dipole moment tensor D^{ab} and the spin four-tensor S^{ab} is formulated in the form of the generalized Uhlenbeck-Goudsmit hypothesis, D^{ab}=g_{S}S^{ab}. It is also found that the spin four-tensor S^{ab} can be decomposed into two 4-vectors, the usual `space-space' intrinsic angular momentum S^{a}, which will be called `magnetic' spin (mspin), and a new one, the `time-space' intrinsic angular momentum Z^{a}, which will be called `electric' spin (espin). Both spins are equally good physical quantities. Taking into account the generalized Uhlenbeck-Goudsmit hypothesis, the decomposition of S^{ab} and the decomposition of D^{ab} into the dipole moments m^{a} and d^{a}, we find that an electric dipole moment (EDM) of a fundamental particle, as a four-dimensional (4D) geometric quantity, is determined by Z^{a} and not, as generally accepted, by the spin $\mathbf{S}$ as a 3-vector. Also it is shown that neither the T inversion nor the P inversion are good symmetries in the 4D spacetime. In this geometric approach, only the world parity W, Wx^{a}=-x^{a}, is well defined in the 4D spacetime. Some consequences for elementary particle theories and experiments that search for EDM are briefly discussed.