Tables of the Su(Mn) ⊃ Su(M) X Su(N) Coefficients of Fractional Parentage

The f₂-particle coefficients of fractional parentage for the group chain SU(mn) ⊃ SU(m) x SU(n) or U(mn) ⊃ U(m) x U(n), with arbitrary m and n and with as many as possible symmetries, are tabulated for systems with up to six particles and for f₂ equal up to three. All the coefficients are in the form of square roots of simple fractions. The algorithm for the CPF as well as the symmetries of the CFP are discussed.

• The Algorithm:
  • The SU(mn) ⊃ SU(m) x SU(n) Coefficients of Fractional Parentage
  • The CG Coefficients of Permutation Groups
  • The S(f) ⊃ S (f₁) x S (f₂) ISF
  • The Calculation Formula for the CFP
  • The Properties of the CFP
  • The Phase Convention
  • The Evaluation of the CFP
  • Discussion
  • Appendix
• The Use of the Tables
• Tables
• References