Relation of a unified quantum field theory of spinors to the structure of general relativity

Based on a unified quantum field theory of spinors assumed to describe all matter fields and their interactions we construct the space-time structure of general relativity according to a general connection within the corresponding spinor space. The tetrad field and the corresponding metric field are composed from a space-time dependent basis of spinors within the internal space of the fundamental matter field. Similar to twistor theory the Minkowski signature of the space-time metric is related to this spinor nature of elementary matter, if we assume the spinor space to be endowed with a symplectic structure. The equivalence principle and the property of background independence arise from the fact that all elementary fields are composed from the fundamental spinor field. This means that the structure of space-time according to general relativity seems to be a consequence of a fundamental theory of matter fields and not a presupposition as in the usual setting of relativistic quantum field theories.

Figure 1

Feynman graph of the self-interacting fundamental spinor field: The horizontal double line represents a composed state from a spinor state describing a particle and a spinor state describing an antiparticle. At the vertices there coincide a state of a free particle and a state of a free antiparticle moving backwards in time.

Figure 2

Hierarchy of space-time structure: At the beginning there is only assumed the structure of a differential manifold. On this manifold representing space-time there is defined a spinor field and the metric properties of space-time are derived from the properties of this abstract space of the spinor field.