# Conformal structures and twistors in the paravector model of spacetime

@article{Rocha2004ConformalSA,
title={Conformal structures and twistors in the paravector model of spacetime},
author={Rold{\~a}o da Rocha and Jayme Vaz},
journal={International Journal of Geometric Methods in Modern Physics},
year={2004},
volume={04},
pages={547-576}
}
• Published 21 December 2004
• Mathematics
• International Journal of Geometric Methods in Modern Physics
Some properties of the Clifford algebras and are presented, and three isomorphisms between the Dirac–Clifford algebra and are exhibited, in order to construct conformal maps and twistors, using the paravector model of spacetime. The isomorphism between the twistor space inner product isometry group SU(2,2) and the group $pin+(2,4) is also investigated, in the light of a suitable isomorphism between and . After reviewing the conformal spacetime structure, conformal maps are described in… 14 Citations Two-Component Spinorial Formalism Using Quaternions for Six-Dimensional Spacetimes • Mathematics Advances in Applied Clifford Algebras • 2021 In this article we construct and discuss several aspects of the two-component spinorial formalism for six-dimensional spacetimes, in which chiral spinors are represented by objects with two Spinorial wave equations and stability of the Milne spacetime • Mathematics • 2015 The spinorial versions of the conformal vacuum Einstein field equations are used to construct a system of quasilinear wave equations for the various conformal fields. As a part of the analysis we The Complex Algebra of Physical Space: A Framework for Relativity • Mathematics • 2012 A complex and, equivalently, hyperbolic extension of the algebra of physical space (APS) is discussed that allows one to distinguish space-time vectors from paravectors of APS, while preserving the ELKO, Flagpole and Flag-Dipole Spinor Fields, and the Instanton Hopf Fibration • Mathematics • 2010 Abstract.In a previous paper we explicitly constructed a mapping that leads Dirac spinor fields to the dual-helicity eigenspinors of the charge conjugation operator (ELKO spinor fields). ELKO spinor The Clifford Algebra Approach to Quantum Mechanics B: The Dirac Particle and its relation to the Bohm Approach • Physics • 2010 In this paper we present for the first time a complete description of the Bohm model of the Dirac particle. This result demonstrates again that the common perception that it is not possible to Conformal relativity with hypercomplex variables • S. Ulrych • Physics Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences • 2014 Majorana's arbitrary spin theory is considered in a hyperbolic complex representation. The underlying differential equation is embedded into the gauge field theories of Sachs and Carmeli. In START in a Five-Dimensional Conformal Domain In this paper we give a brief review of the pseudo-Riemannian geometry of the five-dimensional homogeneous space for the conformal group O(4, 2). Its topology is described and its relation to the Projective View on Motion Groups I: Kinematics and Relativity • D. Brezov • Mathematics Advances in Applied Clifford Algebras • 2019 The paper provides a consistent study on the projective construction of low-dimensional motion groups starting with $$\mathrm {SO}(3)$$SO(3) and then gradually extending to the Galilean and Complexifying the Spacetime Algebra by Means of an Extra Timelike Dimension: Pin, Spin and Algebraic Spinors Because of the isomorphism$\operatorname{Cl}_{1,3}(\Bbb{C})\cong\operatorname{Cl}_{2,3}(\Bbb{R})$, it is possible to complexify the spacetime Clifford algebra$\operatorname{Cl}_{1,3}(\Bbb{R})\$ by

## References

SHOWING 1-10 OF 81 REFERENCES
Twistors, Generalizations and Exceptional Structures
• Mathematics
• 2004
This paper is intended to describe twistors via the paravector model of Clifford algebras and to relate such description to conformal maps in the Clifford algebra over R(4,1), besides pointing out
The Paravector Model of Spacetime
The geometric (or Clifford) algebra Cl3 of three-dimensional Euclidean space is endowed with a natural complex structure on a four-dimensional space. If paravectors, which are formed sums of scalars
Clifford algebra: Notes on the spinor metric and Lorentz, Poincaré, and conformal groups
A particular normalization for the set of basis elements {Γ i } of the complex Clifford algebrasC(p,q) is motivated and defined by demanding that the physical bispinor densities ρ i =ΨΓ i Ψ be real.
Revisiting Clifford algebras and spinors I: the twistor group SU(2,2) in the Dirac algebra and some other remarks
• Mathematics
• 2004
This paper is the first one of a series of three, and its main aim is to review some properties of the Clifford algebras Cl3,0, Cl1,3, Cl4,1 ≃ C⊗Cl1,3 and Cl2,4, and exhibit three isomorphisms
Twistor transform in d dimensions and a unifying role for twistors
• Physics
• 2006
Twistors in four dimensions d=4 have provided a convenient description of massless particles with any spin, and this led to remarkable computational techniques in Yang-Mills field theory. Recently it
Clifford algebra approach to twistors
• Mathematics
• 1982
Local particle interpretation or, equivalently, an enlargement of a structure group to the Poincare group at each point of a Riemannian space‐time manifold naturally results in a complexification of
Twistors and the conformal group
The connected symmetry group SU(2, 2) of twistor space (T), a four‐dimensional complex manifold with metric dsT2≡dX0 dX2¯+dX2 dX0¯+dX1 dX3¯+dX3 dX1¯, and the connected symmetry group O0(2, 4) of
The design of linear algebra and geometry
Conventional formulations of linear algebra do not do justice to the fundamental concepts of meet, join, and duality in projective geometry. This defect is corrected by introducing Clifford algebra
Twistor Approach to Relativistic Dynamics and to the Dirac Equation — A Review
Twistors, which can be regarded as spinors of the conformal group acting on compactified Minkowski space, form a relativistic phase space T of a massless particle with a non-vanishing helicity [1]. A
Conformal Lorentz geometry revisited
The group U(2,2) and its subgroup SU(2,2) were considered by Penrose in his study of the conformal compactification M of the Minkowski space M [R. Penrose and W. Rindler, Spinors and Space‐Time