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arXiv:0804.2997 · Physical Review A

Helicity correlations of vector bosons

Paweł Caban

Published Jun 5, 2008• 22 citations

Abstract

We calculate the helicity and polarization correlation functions in the Einstein-Podolsky-Rosen-type experiments with relativistic vector bosons. Obtained results show that surprising behavior of the correlation function reported by Caban, Rembieli\ifmmode \acute{n}\else \'{n}\fi{}ski, and W\l{}odarczyk [Phys. Rev. A 77, 012103 (2008)] is an intrinsic property of relativistic quantum mechanics and not a result of the choice of the spin operator. We show that the linear polarization correlation function in the appropriately chosen state in the massless limit is the same as the correlation function in the scalar two-photon state. We show also that the polarization correlation function violates the Clauser-Horne-Shimony-Holt inequality and that the degree of this violation can increase with the particle momentum and inequality is violated maximally in the massless limit.

DOI: 10.1103/physreva.77.062101

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We calculate the helicity and polarization correlation functions in the Einstein-Podolsky-Rosen-type experiments with relativistic vector bosons. Obtained results show that surprising behavior of the correlation function reported by Caban, Rembieli\ifmmode \acute{n}\else '{n}\fi{}ski, and W\l{}odarczyk [Phys. Rev. A 77, 012103 (2008)] is an intrinsic property of relativistic quantum mechanics and not a result of the choice of the spin operator. We show that the linear polarization correlation function in the appropriately chosen state in the massless limit is the same as the correlation function in the scalar two-photon state. We show also that the polarization correlation function violates the Clauser-Horne-Shimony-Holt inequality and that the degree of this violation can increase with the particle momentum and inequality is violated maximally in the massless limit.

We calculate the polarization correlation function in the Einstein-Podolsky-Rosen--type experiments with relativistic spin-

1/2

particles. This function depends monotonically on the particle momenta. Moreover, we also show that the polarization correlation function violates the Clauser-Horn-Shimony-Holt inequality and the degree of this violation can depend on the particle momenta and the motion of observers.

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.

We calculate the relativistic correlation function for a hybrid system of a photon and a Dirac particle. Such a system can be produced in decay of another spin-

\frac{1}{2}

fermion. We show that the relativistic correlation function, which depends on particle momenta, may have local extrema for fermion velocity of the order

0.5c

. This influences the degree of violation of the Clauser-Horne-Shimony-Holt inequality.

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.

We calculate and investigate the relativistic correlation function for bipartite systems of spin-

1/2

particles in vector states and spin-

1

particles in tensor states. We show that the relativistic correlation function, which depends on particle momenta, may have local extrema. Furthermore, the momentum dependence of the correlation functions for two choices of the relativistic spin operator may be significantly different.

The relativistic spin correlation function was calculated for a pair of electrons originating from M\o{}ller scattering of two polarized electron beams. The results were discussed in view of a possible measurement of the correlation function and the corresponding probabilities. The special case of scattering off a stationary target (both polarized and unpolarized) was also analyzed. It was shown that the Clauser-Horne-Shimony-Holt (CHSH) inequality may be violated in the relativistic energy range when both scattering electrons are highly polarized.