Related papers: Geometry, Zitterbewegung, Quantization
Discrete symmetries, parity, time reversal, antipodal, and charge conjugation transformations for spinor field in de Sitter space, are presented in the ambient space notation, i.e. in a coordinate independent way. The PT and PCT…
The most general 2+1 dimensional spinning particle model is considered. The action functional may involve all the possible first order Poincare invariants of world lines, and the particular class of actions is specified thus the…
Using the hydrodynamical formalism of quantum mechanics for a Schrodinger spinning particle, developed by T. Takabayashi, J. P. Vigier and followers, that involves vortical flows, we propose the new geometrical interpretation of the…
A new concept of geometrization of electromagnetic field is proposed. Instead of the concept of extended field and its point sources, the interacting Maxwellian and Dirac electron--positron fields are considered as a microscopic unified…
The worldline of a free electron is revealed by applying Dirac's velocity operator to its Dirac wave function whose space-time arguments are expressed in a proper time by a Lorentz transformation. This motion can be decomposed into two…
The way a field transforms under rotations determines its statistics--as is easy to see for scalar, Dirac, and vector fields.
The influence of spatial geometry on the vacuum polarization in 2+1-dimensional spinor electrodynamics is investigated. The vacuum angular momentum induced by an external static magnetic field is found to depend on global geometric surface…
It is shown that models of elementary particles in classical general relativity (geons) will naturally have the transformation properties of a spinor if the spacetime manifold is not time orientable. From a purely pragmatic interpretation…
In the Dirac theory for the motion of free relativistic electrons, highly oscillatory components appear in the time evolution of physical observables such as position, velocity, and spin angular momentum. This effect is known as…
The motion of a classical spinning test particle in the field of a weak plane gravitational wave is studied. It is found that the characteristic dimensions of the particle's orbit is sensitive to the ratio of the spin to the mass of the…
We consider an exact Foldy-Wouthuysen transformation for the Dirac spinor field on the combined background of a gravitational wave and constant uniform magnetic field. By taking the classical limit of the spinor field Hamiltonian we arrive…
We consider the theory of spinor fields written in polar form and we re-express it in terms of the so-called 1+1+2 covariant splitting: after this is done for the basic kinematic variables, we proceed to decompose the dynamical equations,…
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…
In gravitation theory, the realistic fermion matter is described by spinor bundles associated with the cotangent bundle of a world manifold $X$. In this case, the Dirac operator can be introduced. There is the 1:1 correspondence between…
Spinors have played an essential but enigmatic role in modern physics since their discovery. Now that quantum-gravitational theories have started to become available, the inclusion of a description of spin in the development is natural and…
The dynamics of pseudo-classical spinning particles in spacetime of gravitational plane waves of general polarization and harmonic profile is studied. The resulting equations of motion are solved exactly and the results are compared with…
These notes address the planar gravitational wave solutions of general relativity in empty space-time, and analyze the motion of test particles in the gravitational wave field. Next we consider related solutions of the Einstein equations…
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…
Grassmann-valued Dirac fields together with the electromagnetic field (the pseudoclassical basis of QED) are reformulated on spacelike hypersurfaces in Minkowski spacetime and then restricted to Wigner hyperplanes to get their description…
The aim of the lectures is to introduce first-year Ph.D. students and research workers to the theory of the Dirac operator, spinor techniques, and their relevance for the theory of eigenvalues in Riemannian geometry. Topics: differential…