Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-05-10
Physics
High Energy Physics
High Energy Physics - Theory
13 pages
Scientific paper
We investigate a model in which spinors are considered as being embedded within the Clifford algebra that operates on them. In Minkowski space $M_{1,3}$, we have four independent 4-component spinors, each living in a different minimal left ideal of $Cl(1,3)$. We show that under space inversion, a spinor of one left ideal transforms into a spinor of another left ideal. This brings novel insight to the role of chirality in weak interactions. We demonstrate the latter role by considering an action for a generalized spinor field $\psi^{\alpha i}$ that has not only a spinor index $\alpha$ but also an extra index $i$ running over four ideals. The covariant derivative of $\psi^{\alpha i}$ contains the generalized spin connection, the extra components of which are interpreted as the SU(2) gauge fields of weak interactions and their generalization. We thus arrive at a system that is left-right symmetric due to the presence of a "parallel sector", postulated a long time ago, that contains mirror particles coupled to mirror SU(2) gauge fields.
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