Unified prescription for the generation of electroweak and gravitational gauge field Lagrangian on a principal fiber bundle

Abstract

It is essentially known that useful gauge field Lagrangians arise as Weil polynomials of the curvature of the gauge connection. The deeper implications and details of this fact are worked out in two widely differing cases. The Glashow–Weinberg–Salam gauge field Lagrangian for electroweak theory and the Townsend–Zardecki action for gravitation are obtained from the same type of ‘‘Yang–Mills’’ Weil form on a principal fiber bundle over space-time, with symmetry group U(2) and SO(2,3), respectively. The unified geometrical approach given here shows that fiber bundle reduction and symmetry breaking are essential not only in electroweak theory but also in the SO(2,3) gauge theory for gravitation. In fact, the process of symmetry breaking in electroweak theory and the soldering of the anti-de Sitter bundle, essential in the interpretation of SO(2,3) gauge theory as a theory for gravitation, are corresponding geometrical concepts.