Hubbard-Stratonovich transformations to self-energies with coset decomposition to anomalous pair condensates for the standard model of electroweak interactions

Abstract

The standard model of the strong and electroweak interactions is transformed from the ordinary path integral with the Lagrangians of quarks and leptons and with the Abelian and non-Abelian gauge fields to corresponding self-energies. We apply the precise formulation in terms of massless Majorana Fermi fields with 'Nambu' doubling which naturally leads to the appropriate HST's of the self-energies and to the subsequent coset decomposition for the SSB. The total coset decomposition of the Fermi fields is given by the dimension N0=90 for the symmetry breaking SO(N0,N0)/U(N0)xU(N0) where the densities of fermions, related to the invariant subgroup U(N0), are contained in a background functional for the remaining SO(N0,N0)/U(N0) coset field degrees of freedom.