Related papers: Geometry, Zitterbewegung, Quantization
The kinematic degrees of freedom of spinning particles are analyzed and an explicit construction of the phase space and the simplectic structure that accomodates them is presented. A Poincare invariant theory of classical spinning particles…
We give a geometrical derivation of the Dirac equation by considering a spin-1/2 particle travelling with the speed of light in a cubic spacetime lattice. The mass of the particle acts to flip the multi-component wavefunction at the lattice…
Traditionally, the zitterbewegung (ZB) of the Dirac electron has just been studied at the level of quantum mechanics. Seeing that the fact that an old interest in ZB has recently been rekindled by the investigations on spintronic, graphene,…
The conventional role of spacetime geometry in the description of gravity is pointed out. Global Poincar$\acute{\mbox{e}}$ symmetry as an inner symmetry of field theories defined on a fixed Minkowski spacetime is discussed. Its extension to…
A unified approach to the study of classical and quantum spin in external fields is developed. Understanding the dynamics of particles with spin and dipole moments in arbitrary gravitational, inertial and electromagnetic fields is important…
We consider the coupling between massive and spinning particles and three dimensional gravity. This allows us to construct geometric operators (distances between particles) as Dirac observables. We quantize the system a la loop quantum…
We discuss a mechanism of spin decoherence in gravitation within the framework of general relativity. The spin state of a particle moving in a gravitational field is shown to decohere due to the curvature of spacetime. As an example, we…
Some aspects of Dirac spinors are resumed and studied in order to interpret mathematically the P and T operations in a gravitational field.
A system in which the free part of the action possesses a gauge symmetry that is not respected by the interacting part presents problems when quantized. We illustrate how the Dirac constraint formalism can be used to address this difficulty…
We study some particular modifications of gravity in search for a natural way to unify the gravitational and electromagnetic interaction. The certain components of connection in the appearing variants of the theory can be identified with…
We investigate the quantum motion of a neutral Dirac particle bouncing on a mirror in curved spacetime. We consider different geometries: Rindler, Kasner-Taub and Schwarzschild, and show how to solve the Dirac equation by using geometrical…
The equation describing the stochastic motion of a classical particle in 1+1-dimensional space-time is connected to the Dirac equation with external gauge fields. The effects of assigning different turning probabilities to the forward and…
After a revision of the main features of the structure of the Dirac electron a plausible definition of elementary particle is stated. It is shown that this definition leads in the classical case to a picture which produces a very clear…
The Dirac equation is reinterpreted as a constitutive equation for singularities in the electromagnetic vacuum, with the electron as a point singularity on a lightlike toroidal vortex. The diameter of the vortex is a Compton wavelength and…
We investigate using Clifford algebra methods the theory of algebraic dotted and undotted spinor fields over a Lorentzian spacetime and their realizations as matrix spinor fields, which are the usual dotted and undotted two component spinor…
The Dirac equation is a cornerstone in the history of physics, merging successfully quantum mechanics with special relativity, providing a natural description of the electron spin and predicting the existence of anti-matter. Furthermore, it…
We construct the model with light-like world-lines for the massive 4D spinning particles and 3D anyons. It is obtained via the formal bosonization of pseudoclassical model for the massive Dirac particle with subsequent reduction to the…
Within the framework of classical field theory, the connection between the Dirac field as the field of matter and the spacetime metric is discussed. Polarization structure of the Dirac field is shown to be rich enough to determine the…
Using the language of the Geometric Algebra, we recast the massless Dirac bispinor as a set of Lorentz scalar, bivector, and pseudoscalar fields that obey a generalized form of Maxwell's equations of electromagnetism. The spinor's unusual…
We describe a new phenomenon of zitterbewegung of a free Dirac particle in cosmological spacetimes. Unlike the similar effect theorized by Schrodinger in 1930, the cosmological zitterbewegung is a real, physically attainable effect, which…