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.
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.
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.
This paper was concerned with the spin-momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only two momentum eigen states (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin-momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not observer-dependent quantity in inertial frame. Likewise, we have calculated the measure of entanglement (by using the concurrence) and has shown that entanglement decreases with respect to the increasing of observer velocity. Finally, we argue that, Wigner rotation is induced by Lorentz transformations can be realized as controlling operator.
This paper is concerned with the spin–momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin and momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not an observer-dependent quantity in the inertial frame. Likewise, we have calculated the measure of entanglement (by using the concurrence) and have shown that entanglement decreases with respect to the increase in observer velocity. Finally, we argue that Wigner rotation is induced by Lorentz transformations and can be realized as a controlling operator.
We have studied a relativistically covariant Stern-Gerlach (SG) experiment for a relativistic spin and a Dirac spin. We have obtained the relativistic spin in an arbitrary frame by using the classical spin dipole tensor, which gives the covariant spin dipole interactions, and the relation between a spin and a spin magnetic dipole moment. The relativistic spin is shown to have problems to become a proper spin operator for a massive relativistic particle because of two reasons. First, the relativistic spin three-vector operators cannot satisfy the spin algebra. Second, the SG experiment for the relativistic particle provides a paradox between two observers in the particle rest frame and the laboratory frame, in which the particle is moving. We have shown that the paradox in the SG experiment is resolved by the Dirac spin, which is covariantly defined by a Lorentz transformation in the Dirac spinor representation. The Dirac spin three-vector operators satisfy the spin algebra. It is shown that the SG experiment for the Dirac spin in the inertial frame, where there is only magnetic field, can determine the spin without the information of the momentum of the particle. This shows that the reduced spin density matrix for the Dirac particle can be well-defined by integrating out the momentum degrees of freedom.
One of the most fundamental phenomena of quantum physics is entanglement. It describes an inseparable connection between quantum systems, and properties thereof. In a quantum mechanical description even systems far apart from each other can share a common state. This entanglement of the subsystems, although arising from mathematical principles, is no mere abstract concept, but can be tested in experiment, and be utilized in modern quantum information theory procedures, such as quantum teleportation. In particular, entangled states play a crucial role in testing our understanding of reality, by violating Bell inequalities. While the role of entanglement is well studied in the realm of nonrelativistic quantum mechanics, its significance in a relativistic quantum theory is a relatively new field of interest. In this work the consequences of a relativistic description of quantum entanglement are discussed. We analyze the representations of the symmetry groups of special relativity, i.e. of the Lorentz group, and the Poincaré group, on the Hilbert space of states. We describe how unitary, irreducible representations of the Poincaré group for massive spin 1/2 particles are constructed from representations of Wigner's little group. We then proceed to investigate the role of the Wigner rotations in the transformation of quantum states under a change of inertial reference frame. Considering different partitions of the Hilbert space of 2 particles, we find that the entanglement of the quantum states appears different in different inertial frames, depending on the form of the states, the chosen inertial frames, and the particular choice of partition. It is explained, how, despite of this, the maximally possible violation of Bell inequalities is frame independent, when using appropriate spin observables, which are related to the Pauli-Ljubanski vector, a Casimir operator of the Poincaré group.
Variation of the von Neumann entropy by the Lorentz transformation is discussed. Taking the spin-singlet state in the center-of-mass frame, the von Neumann entropy in the laboratory frame is calculated from the reduced density matrix obtained by taking the trace over 4-momentum after the Lorentz transformation. As the model to discuss the EPR spin correlation, it is supposed that one parent particle splits into a superposition state of various pair states in various directions. Computing the von Neumann entropy and the Shannon entropy, we have shown a global behavior of the entropy to see a relativistic effect. We discuss also the superrelativistic limit, distinguishability between the two particles of the pair and so on.