Abstract In this paper we study the single particle entanglement induced by a Lorentz boost. We described the particle as a solution of the free Dirac equation, a Dirac bispinor, and compare the induced momentum-spin entanglement with the result obtained in the widely considered framework of relativistic spin 1/2 states. The spin linear entropy for both approaches agree in the ultra relativistic limit. We also verify that the spin-momentum entanglement differers from the spin entropy for the bispinorial case, indicating a true multipartite entanglement involving the degrees of freedom of a Dirac bispinor state: momentum, spin and intrinsic parity. The fact that Dirac bispinors belongs to an irreducible representation of the complete Lorentz group, which also included parity as a symmetry, is the ultimate reason behind such non-trivial structure.Abstract In this paper we study the single particle entanglement induced by a Lorentz boost. We described the particle as a solution of the free Dirac equation, a Dirac bispinor, and compare the induced momentum-spin entanglement with the result obtained in the widely considered framework of relativistic spin 1/2 states. The spin linear entropy for both approaches agree in the ultra relativistic limit. We also verify that the spin-momentum entanglement differers from the spin entropy for the bispinorial case, indicating a true multipartite entanglement involving the degrees of freedom of a Dirac bispinor state: momentum, spin and intrinsic parity. The fact that Dirac bispinors belongs to an irreducible representation of the complete Lorentz group, which also included parity as a symmetry, is the ultimate reason behind such non-trivial structure.

Journal of Physics Conference SeriesAug 1, 20204 citations

A spin observable for a Dirac particle

Paweł Caban, Jakub Rembieliński, Marta Włodarczyk

Annals of PhysicsDec 11, 201217 citations

Relativistic effects on the spin entanglement of two massive Dirac particles

Taeseung Choi, Jin Mok Hur, Jaewan Kim

We have studied the relativistic effect on the spin state of a massive Dirac particle under an arbitrary Lorentz transformation using the Foldy-Woutheysen representation. We have obtained the transformation matrix from the state of a massive Dirac particle with an initial momentum to a state with a transformed momentum under an arbitrary homogeneous Lorentz transformation. We have shown moving observers obtain the consistent monotonic behavior between the concurrence and the maximum value of Bell parameter for the spin state of the pair of particles.We have studied the relativistic effect on the spin state of a massive Dirac particle under an arbitrary Lorentz transformation using the Foldy-Woutheysen representation. We have obtained the transformation matrix from the state of a massive Dirac particle with an initial momentum to a state with a transformed momentum under an arbitrary homogeneous Lorentz transformation. We have shown moving observers obtain the consistent monotonic behavior between the concurrence and the maximum value of Bell parameter for the spin state of the pair of particles.

arXiv:1008.3447Physical Review AJul 27, 201122 citations

Quantum Mechanics of Dirac Particles

World Scientific lecture notes in physicsSep 1, 20200 citations

Spin operator and spin states in Galilean covariant Fermi field theories

Fuad M. Saradzhev

Spin degrees of freedom of the Galilean covariant Dirac field in $(4+1)$ dimensions and its nonrelativistic counterpart in $(3+1)$ dimensions are examined. Two standard choices of spin operator, the Galilean covariant and Dirac spin operators, are considered. It is shown that the Dirac spin of the Galilean covariant Dirac field in $(4+1)$ dimensions is not conserved, and the role of non-Galilean boosts in its nonconservation is stressed out. After reduction to $(3+1)$ dimensions the Dirac field turns into a nonrelativistic Fermi field with a conserved Dirac spin. A generalized form of the L\'evy-Leblond equations for the Fermi field is given. One-particle spin states are constructed. A particle-antiparticle system is discussed.Spin degrees of freedom of the Galilean covariant Dirac field in $(4+1)$ dimensions and its nonrelativistic counterpart in $(3+1)$ dimensions are examined. Two standard choices of spin operator, the Galilean covariant and Dirac spin operators, are considered. It is shown that the Dirac spin of the Galilean covariant Dirac field in $(4+1)$ dimensions is not conserved, and the role of non-Galilean boosts in its nonconservation is stressed out. After reduction to $(3+1)$ dimensions the Dirac field turns into a nonrelativistic Fermi field with a conserved Dirac spin. A generalized form of the L\'evy-Leblond equations for the Fermi field is given. One-particle spin states are constructed. A particle-antiparticle system is discussed.

arXiv:1109.4899Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsDec 20, 20112 citations

Spin degrees of freedom of the Galilean covariant Dirac field in

(4+1)

dimensions and its nonrelativistic counterpart in

(3+1)

dimensions are examined. Two standard choices of spin operator, the Galilean covariant and Dirac spin operators, are considered. It is shown that the Dirac spin of the Galilean covariant Dirac field in

(4+1)

dimensions is not conserved, and the role of non-Galilean boosts in its nonconservation is stressed out. After reduction to

(3+1)

dimensions the Dirac field turns into a nonrelativistic Fermi field with a conserved Dirac spin. A generalized form of the L\'evy-Leblond equations for the Fermi field is given. One-particle spin states are constructed. A particle-antiparticle system is discussed.