low you to move pieces across the board to distant locations. In short, a gauge symmetry such as that in electromagnetism, or in the more esoteric Yang-Mills proposal, only works if the new fields re- quired by the symmetry are massless. Amid all the mathematical com- plexity, this one fact is inviolate.

particular mathematical prop- erty of matrices that makes multiplying them different from multiplying numbers—or, in deference to Yang and Mills, a Yang-Mills symmetry. Yang and Mills's article appears at first glance to be an abstract—or purely speculative—mathematical exploration of the implications of

Strong Interactions." Sakurai took the 2P_GrealestSleryEverTold_AC.indd 192 12/16116 3:06 PIA EFTA00286114 Living inside a Superconductor 193 Yang-Mills suggestion seriously and tried to explore precisely which photonlike particles might convey a strong force between protons and neutrons and the oth

ited to try to make sense of the otherwise complex inter- actions between nucleons and other particles. In response to this notion that some kind of Yang-Mills symmetry might be behind the strong interaction, Murray Gell-Mann developed an elegant symmetry scheme he labeled in a Zen-like fashion the Eight-

ulations typically involve spurious gauge dependence that cancels when physical ob- servable are calculated. For example, in a spontaneously broken Yang-Mills theory one may work in the renormaliz- able class of gauges (RE) upon augmenting the Lagrangian with a gauge fixing term Cil = —GaG a /2 where G a

ulations typically involve spurious gauge dependence that cancels when physical ob- servable arc calculated. For example, in a spontaneously broken Yang-Mills theory one may work in the renormaliz- able class of gauges (RO upon augmenting the Lagrangian with a gauge fixing term Cgi = —G°Ga/2 where = (1/