Vector-spinor space and field equations

Abstract

Generalizing the work of Einstein and Mayer, it is assumed that at each point of space-time there exists a vector-spinor space with N_v vector dimensions and N_s spinor dimensions, where N_v=2k and N_s=2 ^k, k⩾3. This space is decomposed into a tangent space with4 vector and4 spinor dimensions and an internal space with N_v−4 vector and N_s−4 spinor dimension. A variational principle leads to field equations for geometric quantities which can be identified with physical fields such as the electromagnetic field, Yang-Mills gauge fields, and wave functions of bosons and fermions.