Related papers: On the physical interpretation of the Dirac wavefu…
In the most general geometric background, we study Dirac spinor fields with particular emphasis given to the explicit form of their gauge momentum and the way in which this can be inverted so to give the expression of the corresponding…
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…
Spinor description for the curvatures of $D=5$ Yang-Mills, Rarita-Schwinger and gravitational fields is elaborated. Restrictions imposed on the curvature spinors by the dynamical equations and Bianchi identities are analyzed. In the absence…
Multivector quantum mechanics utilizes wavefunctions which are Clifford aggregates (e.g. sum of scalar, vector, bivector). This is equivalent to multi- spinors constructed of Dirac matrices, with the representation independent form of the…
Dirac equation for a charged spinor in electromagnetic field is written for special cases of spherically symmetric potentials. This facilitates the introduction of relativistic extensions of shape invariant potential classes. We obtain the…
20-component Petras theory of 1/2-spin particle with anomalous magnetic momentum in presence of external electromagnetic and gravitational fields is investigated. The gravitation field is described as space-time curvature. Correctness of…
The Dirac field is studied in a Lyra space-time background by means of the classical Schwinger Variational Principle. We obtain the equations of motion, establish the conservation laws, and get a scale relation relating the energy-momentum…
The Relativistic Dynamical Inversion technique, a novel tool for finding analytical solutions to the Dirac equation, is written in explicitly covariant form. It is then shown how the technique can be used to make a change from Cartesian to…
The application of the theory of scale relativity to microphysics aims at recovering quantum mechanics as a new non-classical mechanics on a non-derivable space-time. This program was already achieved as regards the Schr\"odinger and Klein…
The gravitating matter is studied within the framework of the non-commutative geometry. The non-commutative Einstein-Hilbert action on the product of a four dimensional manifold with a discrete space gives the models of matter fields…
We discuss from scratch the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state.…
On the basis of our recent modifications of the Dirac formalism we generalize the Bargmann-Wigner formalism for higher spins to be compatible with other formalisms for bosons. Relations with dual electrodynamics, with the…
We develop a dynamic description of an effective Dirac theory in metamaterials, in which the wavefunction is modeled by the corresponding electric and magnetic field in the metamaterial. This electro-magnetic field can be probed in the…
On the basis of our recent modifications of the Dirac formalism we generalize the Bargmann-Wigner formalism for higher spins to be compatible with other formalisms for bosons. Relations with dual electrodynamics, with the…
We describe a new realization of supersymmetry, called scalar supersymmetry, acting in spaces of differential forms (bi-spinors), where transformation parameters are Lorentz scalars instead of spinors. The realization is related but is not…
A study of fundamental geometrical interactions shows that the Dirac electron can be represented as a conformal wave. A Riemannian space is used, having coordinates that transform locally as spinors. The wave function becomes a gradient.…
The Dirac equation provides a description of spin 1/2 particles, consistent with both the principles of quantum mechanics and of special relativity. Often its presentation to students is based on mathematical propositions that may hide the…
The recent literature shows a renewed interest, with various independent approaches, in the classical theories for spin. Considering the possible interest of those results, at least for the electron case, we purpose in this paper to explore…
The Dirac equation in spherically symmetric fields is separated in two different tetrad frames. One is the standard cartesian (fixed) frame and the second one is the diagonal (rotating) frame. After separating variables in the Dirac…
The known equivalence of 8-dimensional chiral spinors and vectors, also referred to as triality, is discussed for (4+4)-space. Split octonionic representation of SO(4,4) and Spin(4,4) groups and the trilinear invariant form are explicitly…