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

TL;DR

This paper reformulates the standard model's path integral into self-energies using Hubbard-Stratonovich transformations and coset decomposition, providing a new framework for understanding symmetry breaking and fermion densities.

Contribution

It introduces a novel application of Hubbard-Stratonovich transformations and coset decomposition to the standard model, emphasizing self-energies and symmetry breaking in a new formalism.

Findings

Self-energies derived from path integral reformulation.

Coset decomposition characterizes symmetry breaking.

Fermion densities incorporated in background functional.

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.