Related papers: Semiclassical limit for Dirac particles interactin…
This paper presents a relativistic symmetrical interpretation of the Dirac equation in 1+1 dimensions which predicts no zitterbewegung for a free spin-1/2 particle. This could resolve the longstanding puzzle of zitterbewegung in…
The Hamiltonian formulation of the motion of a spinning relativistic particle in an external electromagnetic field is considered. The approach is based on the introduction of new coordinates and their conjugated momenta to describe the spin…
We address the propagation of the spin along classical trajectories for a 1/2-spin particle obeying the Dirac equation with scalar potentials. Focusing on classical trajectories as the exact propagation of wave-function discontinuities we…
Nondecaying bound states of elementary spin-half particles are validated and calculated numerically for the Schwarzschild gravitational field using a self-conjugate Hamiltonian with a flat scalar product for any value of the gravitational…
The motion of neutral particles with magnetic moments in an inhomogeneous magnetic field is described in a semi-classical framework. The concept of Coherent Internal States is used in the formulation of the semiclassical approximation from…
We study the semiclassical limit of the two-dimensional Dirac--Hartree equation in the presence of a periodic external potential. The spinor dynamics are formulated using the matrix-valued Wigner transform together with spectral projectors…
We prove the mathematically rigorous (semi-)classical limit $\hbar \to 0$ of the Dirac equation with time-dependent external electromagnetic field to relativistic Vlasov equations with Lorentz force for electrons and positrons. In this…
The helicity flip of a spin-${\textstyle \frac{1}{2}}$ Dirac particle interacting gravitationally with a scalar field is analyzed in the context of linearized quantum gravity. It is shown that massive fermions may have their helicity…
We establish covariant semiclassical transport equations of massive spin-1/2 particles which are generated by the quantum kinetic equation modified by enthalpy current dependent terms. The purpose of modification is to take into account the…
In Dirac materials, the low energy excitations obey the relativistic Dirac equation. This dependence implies that the electrons are exposed to strong spin-orbit coupling. Hence, real spin conservation is believed to be violated in Dirac…
This study explores the Feshbach-Villars (FV) formalism for spin-1/2 particles in curved spacetime. We derive the Hamiltonian form of the Dirac equation in this context and extend the FV transformation accordingly. The generalized…
We prove the possibility of existence of stationary bound states of spin-half particles in the Reissner-Nordstroem gravitational field using a self-conjugate Hamiltonian with a flat scalar product of wave functions. Bound states of Dirac…
The so-called Dirac oscillator was proposed as a modification of the free Dirac equation which reproduces many of the properties of the simple harmonic oscillator but accompanied by a strong spin-orbit coupling term. It has yet to be…
We propose a relativistic particle model without Grassmann variables which, being canonically quantized, leads to the Dirac equation. Both $\Gamma$\,-matrices and the relativistic spin tensor are produced through the canonical quantization…
It is shown that the manner of introducing theinteraction between a spin 1 particle and external classical gravitational field can be successfully uni- fied with the approach that occurred with regard to a spin 1/2 particle and was first…
The notion of a classical particle is inferred from Dirac quantum fields on a curved space-time, by an eikonal approximation and a localization hypothesis for amplitudes. This procedure allows to define a semi-classical version of the…
The formalism of Operational Dynamical Modeling [Phys. Rev. Lett. {\bf 109}, 190403 (2012)] is employed to analyze dynamics of spin half relativistic particles. We arrive at the Dirac equation from specially constructed relativistic…
Hamiltonians describing the relativistic quantum dynamics of a particle with an arbitrary spin are shown to exhibit a supersymmetric structure when the even and odd elements of the Hamiltonian commute. For such supersymmetric Hamiltonians…
We study vacuum polarisation effects of a Dirac field coupled to an external scalar field and derive a semi-classical expansion of the regu-larised vacuum energy. The leading order of this expansion is given by a classical formula due to…
The domain of wave functions and effective potentials of the Dirac and Klein-Gordon equations for quantum-mechanical particles in static centrally symmetric gravitational fields are analyzed by taking into account the Hilbert causality…