The role of superconductivity in development of the Standard Model

In 1986, Steven Weinberg published an article, Superconductivity for Particular Theorists, in which he stated

"No one did more than Nambu to bring the idea of spontaneously broken symmetries to the attention of elementary particle physicists. And, as he acknowledged in his ground-breaking 1960 article  "Axial Current Conservation in Weak Interactions'', Nambu was guided in this work by an analogy with the theory of superconductivity,..."

In the 1960 PRL, referenced by Weinberg, Nambu states that in the BCS theory, as refined by Bogoliubov, [and Anderson]

"gauge invariance, the energy gap, and the collective excitations are logically related to each other as was shown by the author. [Y. Nambu, Phys. Rev. 117, 648 (1960)] In the present case we have only to replace them by (chiral) (gamma_5) invariance, baryon mass, and the mesons." 

This connection is worked out explicitly in two papers in 1961. The first is

Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I

Y. Nambu and G. Jona-Lasinio

They acknowledge, 

"that the model treated here is not realistic enough to be compared with the actual nucleon problem. Our purpose was to show that a new possibility exists for field theory to be richer and more complex than has been hitherto envisaged,"

Hence, I consider this to be a toy model for an emergent phenomena.

The model consists of a massless fermion field with a quartic interaction that has chiral invariance, i.e., unchanged by global gauge transformations associated with the gamma_5 matrix. (The Lagrangian is given above.) At the mean-field level, this symmetry is broken. Excitations include massless bosons (associated with the symmetry breaking and similar to those found earlier by Goldstone) and bound fermion pairs. It was conjectured that these could be analogues of mesons and baryons, respectively. The model was proposed before quarks and QCD. Now, the fermion degrees of freedom would be identified with quarks, and the model illustrates the dynamical generation of quark masses. When generalised to include SU(2) or SU(3) symmetry the model is considered to be an effective field theory for QCD, such as chiral effective theory.