Consider three spin- nucleons (a simplified model of the triton

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Quantum Mechanics · Symmetry, angular momentum and spin

Invariance, Ch Representations of Lie algebras: spin, products and SU(3)

Problem

Consider three spin-12\tfrac12 nucleons (a simplified model of the triton, ignoring isospin and orbital motion), each carrying the two-dimensional representation j=12j=\tfrac12 of su(2)\mathfrak{su}(2). Using the Clebsch-Gordan series χj1χj2=∑jχj\chi_{j_1}\chi_{j_2}=\sum_j\chi_j applied twice, decompose the eight-dimensional product 12⊗12⊗12\tfrac12\otimes\tfrac12\otimes\tfrac12 into irreducible representations of total spin jj, and check that the dimensions sum to 88.

Related theory

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