Spin operator in the Dirac theory

Abstract

We find all spin operators for a Dirac particle satisfying the following very general conditions: (i) spin does not convert positive (negative) energy states into negative (positive) energy states, (ii) spin is a pseudo-vector, and (iii) eigenvalues of the projection of a spin operator on an arbitrary direction are independent of this direction (isotropy condition). We show that there are four such operators and all of them fulfill the standard su(2) Lie algebra commutation relations. Nevertheless, only one of them has a proper non-relativistic limit and acts in the same way on negative and positive energy states. We show also that this operator is equivalent to the Newton-Wigner spin operator and Foldy-Wouthuysen mean-spin operator. We also discuss another operators proposed in the literature.Comment: 9 page

A project to measure quantum spin correlations of relativistic electron pairs in Møller scattering

“…The probabilities P s1 s2 are the primary subject of our measurement using the method of Mott polarimetry (below). Calculations regarding the correlation function and the corresponding probabilities, in the context of the present project, have already been completed [26] and also reported at this Conference [27]. As an example, the dependence of P ++ , P −− , P −+ and P +− on beam energy is shown in fig.…”

“…Since the pioneering paper by Czachor [6] one can notice a raise of interest in relativistic aspects of the quantum information theory, expressed in the most important papers on that subject [6,[9][10][11][12][13], including the papers of our group [7,8,[14][15][16][17][18][19]. However, the theoretical analysis of spin correlations in relativistic regime given in these papers is full of ambiguities and interpretational difficulties.…”

“…They arise mostly due to the fact of an apparent conflict between nonlocality of the relativistic quantum mechanics and the Lorentz symmetry. Rembieliński et al exhaustively discussed the a e-mail: cib@fuw.edu.pl relativistic EPR correlation function for a bipartite system of spin-1/2 fermions in the framework of the relativistic quantum mechanics [17] and the quantum field theory [18]. The function was calculated in both pseudoscalar and vector state, which are the relativistic counterparts of the non-relativistic singlet and triplet states, respectively.…”

“…The observed effect was also found for many other systems. An analysis of spin correlations in bipartite systems of spin-1/2 and spin-1 particles was performed [20]. The correlation functions were calculated for states which are not Lorentz scalars, for two different choices of relativistic spin projection operators.…”

Quantum spin correlations in relativistic Møller scattering

“…This is why we decided to use a state originating from Møller scattering of a polarized electron beam on a target. It is neither maximally entangled nor pure, but it is well defined and it has been shown [15] that the difference between relativistic and non-relativistic correlation function is measurable in this particular case. Although the state before the scattering is fully separable, after the scattering the particles become entangled.…”