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Name: Charles
Status: student
Age: 20s
Location: N/A
Country: N/A
Date: 1999 

Hi, I've got a question about isospin and quark generations: Isospin was originally conceived as a defining quality to differentiate between protons and neutrons, but with the advent of quark-parton theory it became irrelevant to them and was instead adopted by the quarks to differentiate between U and D. Now, what I want to know is: how is it that the first generation has a special device solely to divide U from D, but with second and third generation quarks they can have such things as strangeness or topness, but no equivalent to isospin (strictly speaking, the second generation is considered to possess hypercharge, Y, but for some reason it isn't used to quite the extent that isospin, T3, is used)? I see no qualitative difference between them which would keep the higher mass quarks from requiring an arbitrarily constructed "isospin"-like parameter just as the first generation does. If isospin is necessary, then so too should some equivalent be for the heavier quarks... say ortho-spin and para-spin, (...hypercharge...) or something. Is there something I'm missing, perhaps a difference in some sort of presumed internal structure between that of light quarks and of heavy quarks?

You gotta remember that isospin is an artificial quantum number invented to allow protons and neutrons to be regarded as different states of a single particle, without having multiple-nucleon wavefunctions continually running afoul of the Pauli Exclusion principle. There's a strong motivation for doing this, because the nuclear force happens to be almost blind to the difference between protons and neutrons. Since protons and neutrons are made up of U and D quarks, it's natural that the convenient fiction is continued there. Any two-level system can be cast in terms of an operator that acts like an angular momentum, as Merzbacher shows in his chapters on spin and the dynamics of two-level systems (in "Quantum Mechanics", Wiley). But this doesn't mean that all two-level systems must be viewed in that way.

Tim Mooney

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