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.