Abstract
By using legs comection the general relativistic Dirac equation that is invariant under the general coordinate transformations and spin transformations is investigated. The four-dimensional representation for the generalized Dirac matrices is obtained by introducing the six legs and the concept of sedenion conjugate. It is shown that FermiFermi interaction term must be added to the original Lagrangian density if the legs comection is regarded as an independent field quantity; the electromagnetic field is introduced in comection with the complex legs; and the relation between the spin transformation and Pauli-Guirsey type transformation is considered. (auth)
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