BCS-like action and Lagrangian from the gradient expansion of the determinant of Fermi fields in QCD type, non-Abelian gauge theories with chiral anomalies

TL;DR

This paper derives an effective field theory for BCS quark pairs in QCD-like theories, revealing a close relation to Skyrme-Faddeev field theory with nontrivial Hopf mappings, based on a gradient expansion of fermionic determinants.

Contribution

It introduces a novel effective action for BCS quark pairs from QCD path integrals, connecting it to Skyrme-Faddeev theory and non-Abelian gauge anomalies.

Findings

Derived BCS quark pair action from QCD path integral.

Found close relation to Skyrme-Faddeev field theory.

Identified nontrivial Hopf mapping in the effective theory.

Abstract

An effective field theory of BCS quark pairs is derived from an ordinary QCD type path integral with SU(3) non-Abelian gauge fields. We consider the BCS quark pairs as constituents of nuclei and as the remaining degrees of freedom in a coset decomposition SO(M,M)/U(M)xU(M) of a corresponding total self-energy. The underlying dimension 'M=24' is determined by the product of '2' isospin degrees of freedom, by the 4x4 Dirac gamma matrices with factor '4' and the '3' colour degrees of freedom. Finally, we can compare the derived actions of BCS quark pairs with the ordinary Skyrme Lagrangian and attain the astonishing result that our derived effective actions of BCS quark pairs are more closely related to the Skyrme-Faddeev field theory with the nontrivial Hopf mapping.