Space inversion of spinors revisited: A possible explanation of chiral behavior in weak interactions

摘要

We investigate a model in which spinors are considered as being embedded within the Clifford algebra that operates on them. In Minkowski spaceM1,3, we have four independent 4-component spinors, each living in a different minimal left ideal ofCl(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 fieldψαithat has not only a spinor indexαbut also an extra indexirunning over four ideals. The covariant derivative ofψαicontains 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.