Spinor fields in spaces with torsion

Abstract

It is suggested that the short-range interactions lead to a torsion of physical space, as gravitational interactions lead to its curvature. The existence of torsion implies two kinds of parallelism, (+) and (−), which in turn imply two types of spinor field, ψ(+) and ψ(−). If the geometry is symmetric with respect to (+) and (−) parallelisms, then ψ(+) and ψ(−) have no vector or electromagnetic coupling, and the geometry may be called neutral. The simplest neutral geometry with variable torsion is derivable from a Lagrangian in which a pseudoscalar Yukawa field (the torsion potential) is coupled by pseudovector coupling to ψ(+) and ψ(−). If the geometry does not have neutral symmetry, then ψ(+) and ψ(−) behave like a charge doublet. The hypercharge and the parity of this charge doublet are determined by the weight of the spinor under general coordinate transformations. It follows from the model that leptonic ( m = 0) particles are not coupled to the torsion.