INDUCED MASSES AND SPIN SELF-INTERACTION FROM FIVE-DIMENSIONAL EINSTEIN–CARTAN–DIRAC THEORY

Abstract

The Einstein–Cartan theory with a dilaton field coupling arising from five-dimensional principal fiber bundle structure of the metric is investigated. A Dirac type spinor field is coupled to the metric and to translational gauge fields. After the dimensional reduction, the theory introduces a gravitational spin–spin contact interaction coming from the translational degrees of freedom, which is repulsive between Dirac particles whose spins are aligned and attractive when spins are opposed. A classically stable ground state for the dilaton field exists, which is infinitely degenerate with respect to a rescaling of the metric. The induced mass term in the Dirac equation can be interpreted, e.g. as the bare electron mass, as long as we regard this theory as an effective "medium" energy model coming from finite string field theories.