A partly new approach to 2-spinor geometry, recently developped, 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 I present a revised version of the above said geometric tools and field theory, in which the geometric data consist only of a complex vector bundle $S \to M$ with 2-dimensional fibres (all needed structures are functorially derived from $S$; any considered object which is not a functorial construction is assumed to be a dynamical field). Then I consider various developments, concerning some features of the electromagnetic gauge and a partly new covariant description of electroweak geometry and fields. Finally I examine a 2-spinor treatment of optical geometry and geometric optics in curved spacetime, leading to a description of the photon field as a section of the vertical bundle of the bundle of Riemann spheres associated with $S$.\end

1991 MSC: 81R20, 53C07, 81R25, 83C60, 83C22, 81V15,78A05.

Keywords: two-spinors, connections, tetrad gravity, Maxwell-Dirac fields, electroweak fields,
optical geometry, geometric optics.

Recently, A. Jadczyk and I presented a partly new approach to 2-spinors and Einstein-Cartan-Maxwell-Dirac fields. A first, evident difference with respect to the standard 2-spinor setting is more or less formal: the basic concepts are introduced in an intrinsic, coordinate-free way, using precise algebraic and differential geometric notions which may appeal to a mathematically oriented reader. A more substantial difference is that the correspondence between spacetime vectors and Hermitian spinors, rather than being considered as `adapted' to the spacetime metric representing the gravitational field, is viewed as the gravitational field itself. Namely, if $S$ is a complex vector bundle with 2-dimensional fibres, one can formulate a `tetrad-gravity' approach in which the tetrad is valued in the Hermitian sub-bundle $S\bar\vee\bar S \subset S\otimes\bar S$, which carries a natural conformal Minkowski structure ($\bar S$ denotes the `conjugate bundle' of $S$). This makes it possible to include 2-spinor gravitation in a Lagrangian field theory.

One advantage of this approach is that it yields an integrated and complete formulation of Einstein-Cartan-Maxwell-Dirac fields by assuming {\it minimal geometric data}: all the needed geometric structures are derived functorially from $S$, without fixing any extra background field; if we consider an object which is not functorially determined from $S$, then it is a dynamical field of the theory. So, the tetrad is a map $\Theta:TM\to S\bar\vee\bar S$; a linear connection $C$ on $S$ naturally splits into the gravitational and electromagnetic parts; the Dirac field $\psi$ is a section of $W:=S\oplus \bar S^*$ (there is a natural Clifford map $S\bar\vee\bar S \to End(W)$). Even coupling factors naturally arise as covariantly constant sections
of (tensor) powers of a real line bundle $L$, where $L^2:=L\otimes L$ is defined to be the Hermitian subbundle of $(\wedge^2S) \otimes (\wedge^2\bar S)$. This $L$ can be seen as the `space of length units'. An object tensorialized by some power of $L$ corresponds essentially to a `conformal density' of the standard 2-spinor setting.

In general I do not assume a given $\epsilon\in\wedge^2S^*$, or a given Hermitian metric on the fibres of $S$ (by the way, a global fixed $\epsilon$ implies that $\wedge^2S$ is a trivializable bundle, thus ruling out possible topological effects).

If we translate {\it directly} the standard Einstein-Cartan-Maxwell-Dirac theory in terms of the above said fields $\Theta$, $C$ and $\psi$, then we are forced to use $\Theta^{-1}$ (in the standard formulation,
the inverse $g^\#$ of the spacetime metric is essential). However, it has been suggested that a theory which remains non-singular also when $\Theta$ is degenerate may be interesting in view of quantization: it would allow metric signature change, and the degenerate case could be seen as a geometrical basis for a stochastical approach to quantum theory. From the mathematical point of view, the non-singularity requirement constitues a selection criterion which leads to a particularly simple formulation. In particular we have only first order Lagrangians and equations, according to the philosophy of the so-called `Kemmer equations' and related approaches.

The first three parts of this paper are devoted to a revised presentation of the above said results; then I present various developments, including a partly new description of electroweak geometry and fields. The final part contains a partly new treatment of optical geometry and geometric optics in curved spacetime, which aims at a 2-spinor description of photons suitable for applications to covariant quantum field theory.\end