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AbstractAbstract
[en] The covariant differential properties of the split Cayley subalgebra of local real quaternion tetrads is considered. Referred to this local quaternion tetrad several geometrical objects are given in terms of Zorn-Weyl matrices. Associated to a pair of real null vectors we define two-component spinor fields over the curved space and the associated Zorn-Weyl matrices which satisfy the Dirac equation written in terms of the Zorn algebra. The formalism is generalized by considering a field of complex tetrads defining a Hermitian second rank tensor. The real part of this tensor describes the gravitational potentials and the imaginary part the electromagnetic potentials in the Lorentz gauge. The motion of a charged spin zero test body is considered. The Zorn-Weyl algebra associated to this generalized formalism has elements belonging to the full octonion algebra
[pt]
Consideram-se as propriedades diferencias covariantes do desdobramento da subalgebra de Cayley de tetradas quartenionicas reais locais. Dao-se , referidas a essas tetradas quartenionicas locais, varios objetos geometricos em termos de matrizes de Zorn-Weyl. Define-se associado ao par de vetores nulos reais, campos espinoriais a duas componentes sobre o espaco curvo e as matrizes de Zorn-Weyl associadas que satisfazem a equacao de Dirac escrita em termos da algebra de Zorn. Generaliza-se o formalismo considerando em campo de tetradas complexas definindo um tensor de segunda ordem hermitiano. A parte real desse tensor descreve os potenciais gravitacionais e a parte imaginaria os potencias eletromagneticas no 'gauge' Lorentz. Considera-se o movimento de um corpo teste de spin zero carregado. A algebra de Zorn-Weyl associado a esse formalimmo generalizado tem elementos pertencendo a algebra octonionica completaPrimary Subject
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nd; 29 p
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