Related papers: Dirac-Hestenes spinors and Weierstrass representat…
Exact solutions of the Dirac equation, a system of four partial differential equations, are rare. The vast majority of them are for highly symmetric stationary systems. Moreover, only a handful of solutions for time dependent dynamics…
The paper presents a generalized Weierstrass representation for pseudospherical surfaces in terms of 3x3 matrices, using moving frames and loop group decompositions. The construction of all such surfaces, starting from a given…
We rewrite the standard 4-dimensional Dirac equation in terms of quaternionic 2-component spinors, leading to a formalism which treats both massive and massless particles on an equal footing. The resulting unified description has the…
In the 2-spinor formalism, the gravity can be dealt with curvature spinors with four spinor indices. Here we show a new effective method to express the components of curvature spinors in the rank-2 $4 \times 4$ tensor representation for the…
In this paper, we obtain Weierstrass representations for discrete constant mean curvature surfaces in isotropic 3-space, and use this to construct examples with discrete closed-form parametrizations.
In the first part of the paper we give a tensor version of the Dirac equation. In the second part we formulate and analyse a simple model equation which for weak external fields appears to have properties similar to those of the…
In differential geometry of surfaces the Dirac operator appears intrinsically as a tool to address the immersion problem as well as in an extrinsic flavour (that comes with spin transformations to comformally transfrom immersions) and the…
Using complexified quaternions, a formalism without Lorentz frames, and therefore also without vierbeins, for dealing with tensor and spinor fields in curved spacetime is presented. A local U(1) gauge symmetry, which, it is speculated,…
The concepts of compact and projectively-compact spin-local spinor vertices are introduced. Vertices of this type are shown to be space-time spin-local, i.e. their restriction to any finite subset of fields is space-time local. The known…
An introductory theory of frames on finite dimensional quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.
We study manifolds with split-complex structure and apply some general results to the study of Lorentz surfaces. In particular, we apply our results to timelike minimal immersions. The conformal realization of these surfaces is obtained…
The usual ambient space approach to conformal fields is based on identifying the d-dimensional conformal space as the Dirac projective hypercone in a flat d+2-dimensional ambient space. In this work, we explicitly concentrate on singletons…
This article explores the geometric algebra of Minkowski spacetime, and its relationship to the geometric algebra of Euclidean 4-space. Both of these geometric algebras are algebraically isomorphic to the 2x2 matrix algebra over Hamilton's…
These are introductory notes on the study of the Dirac equation in curved spacetime and its relation to hidden symmetries of the dynamics. We present general results on the relation between special spacetime tensors and hidden symmetries,…
A representation of the Lorentz group is given in terms of 4 X 4 matrices defined over a simple non-division algebra. The transformation properties of the corresponding four component spinor are studied, and shown to be equivalent to the…
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 write down an explicit projection that maps any given 4-spinor to a point in 3+1 spacetime while commuting with the Lorentz action. This suggests that a Lorentz invariant theory - including spacetime itself - has a more natural…
We employ the polar decomposition of the Dirac field to describe it as an effective spinorial fluid. We then construct a $(1+1+2)$ covariant formalism for the Dirac field that avoids the introduction of tetrad fields and Clifford matrices.…
The "spin-up" and "spin-down" projections of the second order, chiral form of Dirac Theory are shown to fit a superposition of forms predicted in an earlier classical, complex scalar gauge theory (April, 1992 Class. Quantum Grav.). In some…
We study the generalization of the Willmore functional for surfaces in the three-Heisenberg group. Its construction is based on the spectral theory of the Dirac operator coming to the Weierstrass representation of surfaces (see…