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Kinetic theory of Dirac fermions is studied within the matrix valued differential forms method. It is based on the symplectic form derived by employing the semiclassical wave packet build of the positive energy solutions of the Dirac equation. A satisfactory definition of the distribution matrix elements imposes to work in the basis where the helicity is diagonal which is also needed to attain the massless limit. We show that the kinematic Thomas precession correction can be studied straightforwardly within this approach. It contributes on an equal footing with the Berry gauge fields. In fact in equations of motion it eliminates the terms arising from the Berry gauge fields.
The semiclassical kinetic theory of Dirac particles in the presence of external electromagnetic fields and global rotation is established. To provide the Hamiltonian formulation of Dirac particles a symplectic two-form which is a matrix in spin indic
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 noninerti
A modified quantum kinetic equation which takes account of the noninertial features of rotating frame is proposed. The vector and axial-vector field components of the Wigner function for chiral fluids are worked out in a semiclassical scheme. It is d
We consider the Dirac equation on periodic networks (quantum graphs). The self-adjoint quasi periodic boundary conditions are derived. The secular equation allowing us to find the energy spectrum of the Dirac particles on periodic quantum graphs is o
Hawking radiation from black holes has been studied as a phenomenon of quantum tunneling of particles through their horizons. We have extended this approach to study the tunneling of Dirac particles from a large class of black holes which includes th