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}
}
  • R. Rocha, J. Vaz
  • 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… 
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References

SHOWING 1-10 OF 81 REFERENCES
Twistors, Generalizations and Exceptional Structures
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
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
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
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
...
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