Symmetries

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Symmetries
We next consider isospin symmetry. The
elementary particles form charge multiplets that
are analogous to degenerate spin multiplets in
the hydrogen atom. We assign a charge rotation
analogy to spin called isospin which inherits the
same commutation algebra. We show how isospin can
be used to calculate the relative branching ratio
for strong decays using Clebsch Gordan
coefficients and illustrate an important symmetry
called g- parity which can conveniently determine
whether or not a resonance can decay into an even
or odd number of pions through the strong
interaction.
We look at some basic symmetries of the strong
and electromagnetic interaction including parity,
charge conjugation, and isospin symmetry. Parity
is probably familiar to you from quantum
mechanics. We use it here to limit the possible
form for angular distributions and we demonstrate
that parity is violated in the Lambda decay
which is a weak process. We turn next to charge
conjugation which is an operator that turns
particles into antiparticles. Particles that are
eigenstates of charge conjugation must be self
conjugate with no additive quantum numbers. We
show how this concept can be extended to
fermion-antifermion and boson-antiboson pairs.
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Rotation symmetry and L to pp
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Parity and L ? pp
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Internal symmetries
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C of boson-antiboson pairs
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Selection rule examples
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C of fermion-antifermion pairs
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Isospin symmetry of strong interaction
This symmetry was motivated by the observation
near degeneracy of multiplet states of different
charge. Here is an example for baryons.
The near degeneracy pattern of particle masses is
very reminiscent of the approximate degeneracy of
the hydrogen atom for states with the same
principle QN but different angular momenta. We
speculate there is a symmetry of the strong
interaction that is formally identical to spin or
angular momentum called isospin I. Like spin, the
degeneracy is g2I1
We also see a similar pattern for the low lying
mesons. We will explain some of the quark wave
function factors later. The are based on isospin
symmetry as well as an approximate symmetry
called SU(3) We note with meson, the particles
are in the same grouping as the antiparticles so
some masses are exactly equal (particle and
antiparticles) and others are approximate
(isospin multiplets).
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Reduced matrix elements
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Strong decay branching ratios
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Constructing total I2
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Constructing total I2
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Finding eigenstates of I2
Remaining eigenstates from 2 by 2 partition
diagonalization
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But there is a more practical way...
Here is how to read the one I posted
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Completeness and real phase gives both series
Two tables for the price of one since you can
decompose either the rows or the columns
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More examples
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Isospin violation
Using
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G-parity
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G-parity and quark wave functions
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Quark wf (continued)