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Steve Huntsman
Steve Huntsman
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I'm not sure about the mathematical origins, but the original physical motivation was Yang and Lee'sMills's attempt to deal with the approximate SU(2)-symmetry of nucleons (protons and neutrons). The big step was (as I understand it) when Gell-Mann (and Ne'eman, independently at about the same time) realized that a diagram labeling experimentally observed particles was the weight diagram for SU(3). He made some predictions at a conference:

following the presentation on Strong interactions of strange particles by G. A. Snow, both Ne'eman and Gell-Mann raised their hands to ask for permission to speak. The chairman called Gell-Mann, who was the more eminent physicist of both, and Gell-Mann announced that "[...] we should look for the last particle called, say, Ω-, with S=-3, I=0. [Here, I is isospin.] At 1685 MeV it would be metastable and should decay by weak interaction [...]"

and the rest was the eightfold way.

Of course, principal $G$-bundles and the connections on them had been around for quite some time before (Simons famously pointed this fact out to Yang later on).

I'm not sure about the mathematical origins, but the original physical motivation was Yang and Lee's attempt to deal with the approximate SU(2)-symmetry of nucleons (protons and neutrons). The big step was (as I understand it) when Gell-Mann (and Ne'eman, independently at about the same time) realized that a diagram labeling experimentally observed particles was the weight diagram for SU(3). He made some predictions at a conference:

following the presentation on Strong interactions of strange particles by G. A. Snow, both Ne'eman and Gell-Mann raised their hands to ask for permission to speak. The chairman called Gell-Mann, who was the more eminent physicist of both, and Gell-Mann announced that "[...] we should look for the last particle called, say, Ω-, with S=-3, I=0. [Here, I is isospin.] At 1685 MeV it would be metastable and should decay by weak interaction [...]"

and the rest was the eightfold way.

Of course, principal $G$-bundles and the connections on them had been around for quite some time before (Simons famously pointed this fact out to Yang).

I'm not sure about the mathematical origins, but the original physical motivation was Yang and Mills's attempt to deal with the approximate SU(2)-symmetry of nucleons (protons and neutrons). The big step was (as I understand it) when Gell-Mann (and Ne'eman, independently at about the same time) realized that a diagram labeling experimentally observed particles was the weight diagram for SU(3). He made some predictions at a conference:

following the presentation on Strong interactions of strange particles by G. A. Snow, both Ne'eman and Gell-Mann raised their hands to ask for permission to speak. The chairman called Gell-Mann, who was the more eminent physicist of both, and Gell-Mann announced that "[...] we should look for the last particle called, say, Ω-, with S=-3, I=0. [Here, I is isospin.] At 1685 MeV it would be metastable and should decay by weak interaction [...]"

and the rest was the eightfold way.

Of course, principal $G$-bundles and the connections on them had been around for quite some time before (Simons famously pointed this fact out to Yang later on).

Source Link
Steve Huntsman
Steve Huntsman
  • 15.4k
  • 7
  • 75
  • 130

I'm not sure about the mathematical origins, but the original physical motivation was Yang and Lee's attempt to deal with the approximate SU(2)-symmetry of nucleons (protons and neutrons). The big step was (as I understand it) when Gell-Mann (and Ne'eman, independently at about the same time) realized that a diagram labeling experimentally observed particles was the weight diagram for SU(3). He made some predictions at a conference:

following the presentation on Strong interactions of strange particles by G. A. Snow, both Ne'eman and Gell-Mann raised their hands to ask for permission to speak. The chairman called Gell-Mann, who was the more eminent physicist of both, and Gell-Mann announced that "[...] we should look for the last particle called, say, Ω-, with S=-3, I=0. [Here, I is isospin.] At 1685 MeV it would be metastable and should decay by weak interaction [...]"

and the rest was the eightfold way.

Of course, principal $G$-bundles and the connections on them had been around for quite some time before (Simons famously pointed this fact out to Yang).