Related papers: Higher Derivative Fermionic Field Equation in the …

Maxwell's equations and the Dirac equation are the first-order differential relativistic wave equation for electromagnetic waves and electronic waves respectively. Hence, there is a notable similarity between these two wave equations, which…

On a static spacetime, the solutions of the Dirac equation are generated by a time-independent Hamiltonian. We study this Hamiltonian and characterize the split into positive and negative energy. We use it to find explicit expressions for…

The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. Covariant equations for this motion are demonstrated to possess pathological solutions, when treated nonperturbatively in…

A relativistic wave equation for spin 1/2 particles in the Melvin space-time, a space-time where the metric is determined by a magnectic field, is obtained. The effects of very intense magnetic fields in the energy levels, as intense as the…

Solutions of the Dirac equation for an electron in the Coulomb potential are obtained using operator invariants of the equation, namely the Dirac, Johnson-Lippmann and recently found new invariant. It is demonstrated that these operators…

We derive a Cooper-Frye type spin polarization formula for Dirac fermions at local thermal equilibrium described by a grand canonical ensemble specified by temperature, fluid velocity, chemical potential, and spin potential. We discuss the…

We generalize the worldline formalism to include spin 1/2 fields coupled to gravity. To this purpose we first extend dimensional regularization to supersymmetric nonlinear sigma models in one dimension. We consider a finite propagation time…

Despite fermion doubling, a two-dimensional quasi-relativistic spin-1/2 system can still lead to true fractionalization of electrical charge, when a massive ordered phase supports a "half-vortex". Such topological defect is possible when…

Based on an extension of the Foldy--Wouthuysen method to two-body equations, the problem of expansion of equal-time relativistic equations for two Dirac particles in powers of $1/c$ to higher orders is considered. For the case of two…

A concept of the total velocity that contains velocity and oscillatory velocity is proposed for the velocity solution of Dirac equation. It is shown that the electronic rest energy all comes from the oscillation of the electron itself. For…

We formulate point-particle effective field theory (PPEFT) for relativistic spin-half fermions interacting with a massive, charged finite-sized source using a first-quantized effective field theory for the heavy compact object and a…

The semiclassical limit for Dirac particles interacting with a static gravitational field is investigated. A Foldy-Wouthuysen transformation which diagonalizes at the semiclassical order the Dirac equation for an arbitrary static spacetime…

It is usually supposed that the Dirac and radiation equations predict that the phase of a fermion will rotate through half the angle through which the fermion is rotated, which means, via the measured dynamical and geometrical phase…

Spin current of a Dirac particle is shown to be given by the geometric phase and in terms of the later, a closed form expression is obtained for the dissipationlessness of the spin current.

Previously (A. Akhmeteli, J. Math. Phys., v. 52, p. 082303 (2011)), the Dirac equation in an arbitrary electromagnetic field was shown to be generally equivalent to a fourth-order equation for just one component of the four-component Dirac…

We derive fully explicit equations of motion, and the associated set of constraints, describing the propagation in a flat space-time of a charged spin-3/2 massive state in a constant electromagnetic background. For this purpose, we provide…

This work is a continuation of our recent study of non-relativistic charged particles, confined to a sphere enclosing a magnetic dipole at its center. In this sequel, we extend our computations in two significant ways. The first is to a…

We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…

We have proved on the basis of the symmetry analysis of the standard Dirac equation with nonzero mass that this equation may describe not only fermions of spin 1/2, but also bosons of spin 1. The new bosonic symmetries of the Dirac equation…

We derive and analyze an effective quantum Boltzmann equation in the kinetic regime for the interactions of four distinguishable types of fermionic spin-$\frac{1}{2}$ particles, starting from a general quantum field Hamiltonian. Each…