BREAKING THE SYMMETRY

Yang and Mills had not written their paper as just an esoteric curiosity to serve as a simplified model for Quantum Gravity. Their idea was that this force law had to play a role in the regime of the sub-atomic particles, but, from the very beginning, there had been the question of mass. Yang recalls that Pauli bugged him about it [1]. It was clear that

i) the theory, as it stood, predicted massless vector particles, mutually interacting as if they were charged photons, while

ii) such particles, regardless of whether they refer to ‘ordinary’ electric charge, or to some localized version of isospin, do not exist in Nature, and

iii) the mass is forbidden by gauge-invariance. The very basis of the theory would be destroyed if we simply would add mass terms to the Yang–Mills equations…