A Note on Metric Connections for Chiral and Dirac Spinors
نویسندگان
چکیده
By means of (1.2) and (1.3) each matrix S ∈ SL(2,C) is associated with some matrix S ∈ SO(1, 3,R) so that we can write S = φ(S), see [1], [2], and [3] for detailed description of this construction. Let M be a space-time manifold, i. e. a four-dimensional orientable manifold equipped with a pseudo-Euclidean Minkowski-type metric g and carrying a special smooth geometric structure which is called a polarization. Once some polarization is fixed, one can distinguish the Future light cone from the Past light cone at each point p ∈ M (see [4] for more details). A moving frame (U, Υ0, Υ1, Υ2, Υ3) of the tangent bundle TM is an ordered set of four smooth vector fields Υ0, Υ1, Υ2, Υ3 which are defined and R-linearly independent at each point p of some open subset
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