Weinberg-Salam model as non-Abelian Landau-Ginzburg theory of superconductivity

Abstract

We propose that the Weinberg-Salem model well known as the standard model of the electroweak unification could also describe the non-Abelian ferromagnetic superconductivity made of two-component (spin-up and spin-down) Cooper pair, which could be viewed as the SU(2)xU(1) extension of the Abelian Landau-Ginzburg theory. In this interpretation the two gauge couplings of SU(2) and U(1) (and thus the Weinberg's mixing angle) are completely fixed by the electromagnetic coupling e. And the massless photon in the standard model plays the role of the massless non-Abelian spinon which induces the long range magnetic order and the spin waves in non-Abelian ferromagnetic superconductors. Moreover, the massive Z boson plays the role of the massive photon which generates the well known Meissner effect in ordinary superconductors, and the W boson becomes the charged massive spinon whose mass determines the range of the non-Abelian spin flip interaction in the ferromagnetic superconductors. We discuss the physical implications of the non-Abelian Landau-Ginzburg theory.