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

We show that configurations exist in which the correlation functions and the degree of violation of Bell-type inequalities in the relativistic Einstein-Podolsky-Rosen (EPR) experiment have local extrema for some values of the velocities of the EPR particles. Moreover, this strange behavior can be observed for both discussed relativistic spin operators and for spin-1/2 as well as spin-1 particles. PACS numbers: 03.65 Ta, 03.65 UdUntil recently, almost all papers concerning quantuminformation processing were based on the non-relativistic quantum mechanics. On the other hand the present technological possibilities speed up the investigation of the relativistic aspects of the quantum Einstein-Podolsky-Rosen (EPR) correlations.The aim of this paper is to report some strange behavior of the relativistic EPR correlation functions. We show that the correlation function, which in the relativistic case depends on the particle momenta, for some fixed configurations has local extrema. Such a bechvior has not been reported in the previous works [1,2]. Such extrema can be observed for both spin-1/2 and spin-1 particles and for two different choices of the relativistic spin operator. This suggests that the discussed effect is a general property of the relativistic correlation functions. We also show that relativistic quantum correlations are stronger than nonrelativistic ones for a variety of configurations. Consequently, in such configurations Bell inequalities are more strongly violated by relativistic correlations than by nonrelativistic ones.An appropriate treatment of the EPR experiment is hindered by very serious theoretical and interpretational difficulties concerning the relativistic quantum mechanics. One of the most frustrating problems is the lack of the Lorentz-covariant notion of localizability in the relativistic quantum mechanics. The position operator is needed not only to take into consideration the finite size of the detectors but also it is directly related with the definition and form of spin operator.The most familiar choice of the position operator for a massive particle is the Newton-Wigner operator [3]

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We calculate the joint probabilities and the correlation function in Einstein--Podolsky--Rosen type experiments with a massive vector boson in the framework of quantum field theory. We report on the strange behavior of the correlation function (and the probabilities) -- the correlation function, which in the relativistic case still depends on the particle momenta, for some fixed configurations has local extrema. We also show that relativistic spin-1 particles violate some Bell inequalities more than nonrelativistic ones and that the degree of violation of the Bell inequality is momentum dependent.Comment: 11 pages, 8 figure

In this paper we present and discuss the relativistic correlation function in a bipartite system of two electrons, originating from the e − e − −→ e − e − scattering of a polarized electron beam on an unpolarized target. We also calculate and investigate the probabilities of the definite outcomes of spin-projection measurements performed by two observers. The presented results might help in experimentally verifying whether relativistic quantum theory is able to reproduce the behavior of real quantum systems. PACS number(s): 03.65.Ta, 03.65.Ud I. INTRODUCTIONStarting from the pioneering paper by Czachor [1] one can notice a rise of interest in relativistic aspects of the Einstein-Podolsky-Rosen-type (EPR-type) correlations in systems of massive fermions (see, e.g., Refs. [2-13] and references therein). The behavior of the relativistic correlations is in general different than in the nonrelativistic case. Theoretical analysis showed that relativistic correlations for massive particles may be described by a nonmonotonic function of particle momenta. This unexpected behavior was first found in bipartite vector boson systems and spin-1/2 fermion systems [14,15] and was reflected in the degree of violation of the Bell-type inequalities, which in some configurations was a nonmonotonic function of momentum, too. Moreover, it has been shown that there exist configurations for which the degree of the inequality violation increases with particle momenta and reaches its maximal value in the ultrarelativistic limit. Let us also stress that local extrema do not appear for bipartite photon systems.All the results mentioned previously strongly suggest that the existence of local extrema is a characteristic feature of relativistic correlations for massive particles. For these reasons it is important to measure this correlation function experimentally. Such experiments might be treated as a test of nonlocal aspects of relativistic quantum theory. Thus, the question arises of whether the relativistic corrections can be measured. Our purpose is to show that it is possible to verify the unexpected predictions of relativistic quantum theory mentioned above in the nonlocal correlation experiment by using Møller electrons as the EPR pair.As far as we know, there have been only three correlation experiments to date performed by means of massive relativistic fermions (protons). Their aim was to test Bell-type inequalities. These experiments were the Lamehi-Rachti-Mittig (LRM) experiment [16] performed about thirty years ago at CEN-Saclay and two recent experiments: the first one at the Kernfysisch Versneller Instituut (KVI, Holland) by Hamieh et al. [17] and the second one by Sakai et al. [18] at the RIKEN Accelerator Research Facility (Japan). In all three experiments the proton-proton spin correlations were measured. The LRM