A Note on Connections of the Standard Model in a Gravitation Field

The Standard Model of the theory of elementary particles is based on the U(1) × SU(2) × SU(3) symmetry. In the presence of a gravitation field, i. e. in a non-flat space-time manifold, this symmetry is implemented through three special vector bundles. Connections associated with these vector bundles are studied in this paper. In the Standard Model they are interpreted as gauge fields. 1. The U and SU-bundles and their basic fields. In its canonical form the Standard Model describes elementary particles in the flat Minkowski space-time (see [1– 6]). When passing to a non-flat space-time M we introduce three special vector bundles UM , SUM , and SUM , each equipped with its own basic tensorial fields (see [7]). They are listed in the following table: Symbol Name Bundle Tensorial type D Hermitian metric tensor UM (0, 1|0, 1)