Related papers: Dirac-Hestenes spinor fields in Riemann-Cartan spa…
In this paper, we consider a general twisted-curved space-time hosting Dirac spinors and we take into account the Lorentz covariant polar decomposition of the Dirac spinor field: the corresponding decomposition of the Dirac spinor field…
We show that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), when the three classes of Dirac spinor fields, under Lounesto spinor field classification, are…
The so called Inomata-McKinley spinors are a particular solution of the non-linear Heisenberg equation. In fact, free linear massive (or mass-less) Dirac fields are well known to be represented as a combination of Inomata-McKinley spinors.…
In this second part of the paper, we define spectral spacetimes, a noncommutative generalization of Lorentzian orientable spacetimes of even dimension with a spin structure. There are two main differences with spectral triples: the…
Real Clifford algebras for arbitrary number of space and time dimensions as well as their representations in terms of spinors are reviewed and discussed. The Clifford algebras are classified in terms of isomorphic matrix algebras of real,…
We systematically discuss connections on the spinor bundle of Cahen-Wallach symmetric spaces. A large class of these connections is closely connected to a quadratic relation on Clifford algebras. This relation in turn is associated to the…
It is shown that a subgroup of $SL(2,{\mathbb H})$, denoted $Spin(2,{\mathbb H})$ in this paper, which is defined by two conditions in addition to unit quaternionic determinant, is locally isomorphic to the restricted Lorentz group,…
Dirac operators on curved space-times are introduced with the help of a new point-view that observers have to be included in the formulation of natural laws. The class of Dirac operators are Lorentz invariant in the sense that the…
In this work we analyze the zero mode localization and resonances of $1/2-$spin fermions in co-dimension one Randall-Sundrum braneworld scenarios. We consider delta-like, domain walls and deformed domain walls membranes. Beyond the…
We establish global existence and derive sharp pointwise decay estimates of solutions to cubic Dirac and Dirac-Klein-Gordon systems on a curved background, close to the Minkowski spacetime. By squaring the Dirac operator, we reduce the…
We develop covariant fermionic fields of space-like particles. As an application of the formalism we discuss the example of superluminous tachyons with imaginary rest mass and spin 1/2 forming fermionic ensembles that is relativistically…
From the 16-component Dirac-K\"{a}hler field theory, spinor equations for two types of massless vector photon fields with different parities have been derived. Their equivalent tensor equations in terms of the strength tensor $F_{ab}$ and…
Some properties of the Clifford algebras Cl(3,0), Cl(1,3), Cl(1,3)(C), Cl(4,1) and Cl(2,4) are presented, and three isomorphisms between the Dirac-Clifford algebra C x Cl(1,3) and Cl(4,1) are exhibited, in order to construct conformal maps…
Operator fields in the bundle of Dirac spinors and their conversion to spatial fields are considered. Some commutator equations are studied with the use of the conversion technique.
We establish the spin-statistics theorem for topological quantum field theories (TQFTs) in the framework of Atiyah. We incorporate spin via spin structures on bordisms, and represent statistics using super vector spaces. Unitarity is…
We develop a conformally invariant (CI) framework in $(1+3)$-dimensional de Sitter (dS) spacetime, that unifies the descriptions of graviton, ``partially massless'' graviton, and photon fields. This framework is grounded in a rigorous…
We investigate the modeling capabilities of sets of coupled classical harmonic oscillators (CHO) in the form of a modeling game. The application of simple but restrictive rules of the game lead to conditions for an isomorphism between…
Properties of tensors equivalent to the direct product of two different 4-spinors are investigated. It is shown that the tensors obey additional 8 nonlinear restrictions, those are presented in Lorentz covariant form. In the context of the…
In this article we present the algebraic rearrangement, or matrix inversion of the Dirac equation in a curved Riemann-Cartan spacetime with torsion, the presence of non-vanishing torsion is implied by the intrinsic spin-1/2 of the Dirac…
We investigate the relationship between conformal and spin structure on lorentzian manifolds and see how their compatibility influences the formulation of rigid supersymmetric field theories. In dimensions three, four, six and ten, we show…