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The semiclassical Boltzmann transport equation of charged, massive fermions in a rotating frame of reference, in the presence of external electromagnetic fields is solved in the relaxation time approach to establish the distribution function up to linear order in the electric field in rotating coordinates, centrifugal force and the derivatives. The spin and spin current densities are calculated by means of this distribution function at zero temperature up to the first order. It is shown that the nonequilibrium part of the distribution function yields the spin Hall effect for fermions constrained to move in a plane perpendicular to the angular velocity and magnetic field. Moreover it yields an analogue of Ohm’s law for spin currents whose resistivity depends on the external magnetic field and the angular velocity of the rotating frame. Spin current densities in three-dimensional systems are also established. [ABSTRACT FROM AUTHOR]

A system of multiple spacelike separated Dirac particles is considered and a method for constructing polynomial invariants under the spinor representations of the local proper orthochronous Lorentz groups is described. The method is a generalization of the method used in Johansson (2022) for the case of two Dirac particles. All polynomials constructed by this method are identically zero for product states. The behaviour of the polynomials under local unitary evolution that acts unitarily on any subspace defined by fixed particle momenta is described. By design all of the polynomials have invariant absolute values on this kind of subspaces if the evolution is locally generated by zero-mass Dirac Hamiltonians. Depending on construction some polynomials have invariant absolute values also for the case of nonzero-mass or additional couplings. Because of these properties the polynomials are considered potential candidates for describing the spinor entanglement of multiple Dirac particles, with either zero or arbitrary mass or additional couplings. Polynomials of degree 2 and 4 are derived for the cases of three and four Dirac spinors. For three spinors no non-zero degree 2 polynomials are found but 67 linearly independent polynomials of degree 4 are identified. For four spinors 16 linearly independent polynomials of degree 2 are constructed as well as 26 polynomials of degree 4 selected from a much larger number. The relations of these polynomials to the polynomial spin entanglement invariants of three and four non-relativistic spin- 1 2 particles are described. Moreover, it is described how degree 4 polynomials for five spinors can be constructed and how degree 2 polynomials can be constructed for any even number of spinors. • Method for constructing local Lorentz invariants for multiple Dirac spinors • Locally Lorentz invariant polynomials constructed from skew-symmetric bilinear forms • Constructed polynomials identically zero for all product states • Constructed polynomials invariant up to U(1) phase under different local evolutions [ABSTRACT FROM AUTHOR]

As a follow-up to a recent study in the spin-0 case (Bunao and Galapon, 2015), we construct a one-particle Time of Arrival (TOA) operator conjugate to a Hamiltonian describing a free relativistic spin- 1 / 2 particle in one spatial dimension. Upon transformation in a representation where the Hamiltonian is diagonal, it turns out that the constructed operator consists of an operator term T ˆ whose action is the same as in the spin-0 case, and another operator term T ˆ 0 which commutes with the Hamiltonian but breaks invariance under parity inversion. If we must impose this symmetry on our TOA operator, then we can throw away T ˆ 0 so that the TOA operator is just T ˆ . [ABSTRACT FROM AUTHOR]