Conformal structures and twistors in the paravector model of spacetime

Some properties of the Clifford algebras Cl-3,Cl-0, Cl-1,Cl-3, Cl-4,Cl-1 similar or equal to C circle times Cl-1,Cl-3 and Cl-2,Cl-4 are presented, and three isomorphisms between the Dirac-Clifford algebra C circle times Cl-1,Cl-3 and Cl-4,Cl-1 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 C circle times Cl-1,Cl-3 and Cl-4,Cl-1. After reviewing the conformal spacetime structure, conformal maps are described in Minkowski spacetime as the twisted adjoint representation of $ pin(+)(2,4), acting on paravectors. Twistors are then presented via the paravector model of Clifford algebras and related to conformal maps in the Clifford algebra over the Lorentzian R-4,(1) spacetime.We construct twistors in Minkowski spacetime as algebraic spinors associated with the Dirac-Clifford algebra C circle times Cl-1,Cl-3 using one lower spacetime dimension than standard Clifford algebra formulations, since for this purpose, the Clifford algebra over R-4,R-1 is also used to describe conformal maps, instead of R-2,(4). Our formalism sheds some new light on the use of the paravector model and generalizations.

Pure spinors, twistors, and emergent supersymmetry

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Ten-dimensional super-twistors and Super-Yang-Mills

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estrutura simplética para teorias de spin alto pela descrição de twistors

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

MHV tree amplitudes in super-Yang-Mills and in superstring theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Twistor-like constraints for the superparticle and the superstring

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Twistor-like constraints for the superparticle and the superstring

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)