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Isospin
Name: Charles
Status: student
Age: 20s
Location: N/A
Country: N/A
Date: 1999
Question:
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?
Replies:
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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