Two-spinors, field theories and geometric optics in curved spacetime

A partly new approach to 2-spinor geometry, recently developed, turns out to yield a naturally integrated formulation of Einstein-Cartan and Maxwell-Dirac fields, and to be suitable for describing several topics in field theories which are relevant to covariant quantization on curved spacetime. Here, first a revised version of the above mentioned geometric tools and field theory is presented, in which the geometric data consist only of a complex vector bundle S --> M with two-dimensional fibres (all the needed structures are functorially derived from S; any considered object which is not a functorial construction is assumed to be a dynamical field). Then various developments are considered, concerning some features of the electromagnetic gauge and a partly new covariant description of electroweak geometry and fields. Finally, a 2-spinor treatment of optical geometry and geometric optics in curved spacetime is examined, leading to a description of the photon field as a section of the vertical bundle of the bundle of Riemann spheres associated with S.