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Action for the Dirac spinor field coupled to gravity on noncommutative (NC) Moyal-Weyl space-time is obtained without prior knowledge of the metric tensor. We emphasise gauge origins of gravity (i.e. metric structure) and its interaction…
In this paper we continue our analysis of a formulation of electrodynamics fully covariant under the full Poincar\'e group. Transformations under the four different components of the group force on us the introduction of particles, either…
The purpose of this paper is to investigate several issues concerning the Dirac equation from a time-frequency analysis perspective. More precisely, we provide estimates in weighted modulation and Wiener amalgam spaces for the solutions of…
The triality properties of Dirac spinors are studied, including a construction of the algebra of (complexified) biquaternion. It is proved that there exists a vector-representation of Dirac spinors. The massive Dirac equation in the…
A version of the Dirac equation is derived from first principles using a combination of quaternions and multivariate 4-vectors. The nilpotent form of the operators used allows us to derive explicit expressions for the wavefunctions of free…
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…
Representations of Dirac-Hestenes and Dirac spinor fields via coordinates of surfaces conformally immersed into 4-dimensional complex space are proposed. A relation between time evolution of spinor fields and integrable deformations of…
Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…
The aim of this work is to find exact solutions of the one-dimensional Dirac equation that do not belong to the already known conventional class. We write the spinor wavefunction as a bounded infinite sum in a complete basis set, which is…
We derive new explicit expressions for the Dirac bilinears based on a generic representation of the massive Dirac spinors with canonical polarization. These bilinears depend on a direction $n$ in Minkowski space which specifies the form of…
We write the Dirac equation in curved 4-dimensional Lorentzian spacetime using concepts from the analysis of partial differential equations as opposed to geometric concepts.
When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. Gravitational fields can be incorporated as background spacetime if the…
Our understanding of quantum field theory rests largely on explicit and controlled calculations in perturbation theory. Because of this, much recent effort has been devoted to improve our grasp of perturbative techniques on cosmological…
We reduce Dirac's spinor formalism for a spin 1/2 particle to a complex wavefunction description in curved spacetimes. We consider a localized fermionic particle in curved spacetimes and perform an expansion in terms of the acceleration and…
Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of…
A generalized Clifford manifold is proposed in which there are coordinates not only for the basis vector generators, but for each element of the Clifford group, including the identity scalar. These new quantities are physically interpreted…
We revisit the representation theory of the quantum double of the universal cover of the Lorentz group in 2+1 dimensions, motivated by its role as a deformed Poincar\'e symmetry and symmetry algebra in (2+1)-dimensional quantum gravity. We…
We consider a five-dimensional Einstein--Cartan spacetime upon which Dirac spinor fields can be defined. Dirac spinor fields in five and four dimensions share many features, like the fact that both are described by four-component spinor…
One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for…
While internal space-time symmetries of relativistic particles are dictated by the little groups of the Poincar\'e group, it is possible to construct representations of the little group for massive particles starting from harmonic…