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Springer eBooks

Spin-1/2 Particle

John R. Fanchi

Published Jan 1, 1993• 1 citation
Publisher
DOI
10.1007/978-94-011-1944-3_10

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arXiv:hep-ph/0311081•Nov 6, 2003•0 citations
We study a nonrelativistic system made of two quantum particles constrained to move on a line and a spin located at a fixed point of the line. Initially the two particles are in a maximally entangled state and the spin is down. The first particle interacts with the spin while the second particle is free, i.e., it does not interact neither with the first particle nor with the spin. We rigorously prove that there is a correlation between the state of the spin and the state of the second particle. More precisely, we show that, in a suitable scaling limit, if the first particle flips the spin, then the second particle possesses a definite momentum in the direction opposite to the spin.
The effect of the relativistic spin rotation on two-particle spin states, conditioned by the setting of the spins of the particles in their rest frames and by the noncommutativity of the Lorentz transformations along noncollinear directions, is discussed. Particularly, the transition from the center-of-mass system (c.m.s.) of two spin-1∕2 particles to the laboratory is considered. When the vectors of the c.m.s. particle velocities are not collinear with the velocity vector of the c.m.s., the angles of the relativistic spin rotation for the two particles are different. As a result, the relative fractions of the singlet and triplet states in the relativistic system of two spin-1∕2 particles with a nonzero vector of relative momentum depend on the concrete frame in which the two-particle system is analyzed.
The effect of the relativistic spin rotation, conditioned by the setting of the spin in the rest frame of a particle and by the noncommutativity of the Lorentz transformations along noncolinear directions, is discussed. In connection with this, the Thomas precession of the spin polarization vector at the motion of a particle along a curvilinear trajectory is considered. The transformations of the correlation tensor components for a system of two spin-1/2 particles at the transition from the c.m.s. of the particle pair to the laboratory frame are investigated. When the particle laboratory velocities are not colinear, the relativistic spin rotation angles for these particles are different. As a result, the relative fractions of the singlet and triplet states in the relativistic system of two free spin-1/2 particles with a nonzero vector of relative momentum depend on the concrete frame in which this two-particle system is analyzed.