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.

17 pages, this version is much shorter and all changes are made according to published paper

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Cited by in corpus (5)

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• The Constitutive Relations and the Magnetoelectric Effect for Moving Media
• The Lorentz transformations of the vectors E, B, P, M and the external electric fields from a stationary superconducting wire with a steady current and from a stationary permanent magnet
• The manifestly covariant Aharonov-Bohm effect in terms of the 4D fields
• Electric and magnetic fields as explicitly observer dependent four-dimensional vectors and their Lorentz transformations according to Minkowski-Ivezić