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GROUP THEORY IN PARTICLE PHYSICS

Edward Morell with Professor Zhen Liu�Partially funded by NSF award number PHY-2348668

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GROUPS

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e

a

b

e

e

a

b

a

a

b

e

b

b

e

a

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EXAMPLE: Z₃

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1

2

3

2

3

2

3

1

1

e

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​

​

a: 120°

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​

​

​

b: 240°

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LINEAR REPRESENTATIONS

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LIE GROUPS

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SU(2)

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RAISING/LOWERING OPERATORS

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Highest Weight Construction

  1. Diagonalize J₃
  2. Find the states with highest J₃
  3. Apply the lowering operator to construct the states of the irreducible spin-j representation
  4. Set aside this subspace and focus on those orthogonal to it
  5. Repeat steps 2-4

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Spin 1/2 Spin 1 Spin 3/2

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APPLICATION: CLEBSCH-GORDON COEFFICIENTS

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TOOLS FOR THE JOB

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SPIN 1/2 X 1/2

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SPIN 1 X 1/2

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SPIN 1 X 1/2

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REFERENCES

Howard Georgi – Lie Algebras in Particle Physics