Representation of spinors in the n-dimensional space by a system of tensors

Representation of spinors in n-dimensional space by complex and real systems of tensor

Hestenes' Tetrad and Spin Connections

Defining a spin connection is necessary for formulating Dirac's bispinor equation in a curved space-time. Hestenes has shown that a bispinor field is equivalent to an orthonormal tetrad of vector fields together with a complex scalar field. In this paper, we show that using Hestenes' tetrad for the spin connection in a Riemannian space-time leads to a Yang-Mills formulation of the Dirac Lagrangian in which the bispinor field is mapped to a set of Yang-Mills gauge potentials and a complex scalar field. This result was previously proved for a Minkowski space-time using Fierz identities. As an application we derive several different non-Riemannian spin connections found in the literature directly from an arbitrary linear connection acting on Hestenes' tetrad and scalar fields. We also derive spin connections for which Dirac's bispinor equation is form invariant. Previous work has not considered form invariance of the Dirac equation as a criterion for defining a general spin connection

Interacting spinor and scalar fields in Bianchi type-I Universe filled with viscous fluid: exact and numerical solutions

We consider a self-consistent system of spinor and scalar fields within the framework of a Bianchi type I gravitational field filled with viscous fluid in presence of a $\Lambda$ term. Exact self-consistent solutions to the corresponding spinor, scalar and BI gravitational field equations are obtained in terms of $\tau$, where $\tau$ is the volume scale of BI universe. System of equations for $\tau$ and \ve, where \ve is the energy of the viscous fluid, is deduced. Some special cases allowing exact solutions are thoroughly studied.Comment: 18 pages, 6 figure

Spinor Field in Bianchi type-I Universe: regular solutions

Self-consistent solutions to the nonlinear spinor field equations in General Relativity has been studied for the case of Bianchi type-I (B-I) space-time. It has been shown that, for some special type of nonliearity the model provides regular solution, but this singularity-free solutions are attained at the cost of broken dominant energy condition in Hawking-Penrose theorem. It has also been shown that the introduction of $\Lambda$-term in the Lagrangian generates oscillations of the B-I model, which is not the case in absence of $\Lambda$ term. Moreover, for the linear spinor field, the $\Lambda$ term provides oscillatory solutions, those are regular everywhere, without violating dominant energy condition. Key words: Nonlinear spinor field (NLSF), Bianch type -I model (B-I), $\Lambda$ term PACS 98.80.C CosmologyComment: RevTex, 21 page