manyisospin

◼ manyisospin[{c1, c2, c3},{i1, i2, i2}] returns X, Y, and Z components of the total isospin, as well as the total isospin operator squared, for levels corresponding to a list of operators given as the argument. The phase indexes of the operators must be given as the second argument.

◼ Operators must be expressed in a form which excludes the first index (creation/annihilation) and the last index (spin).

◼ If the list of indexes is not provided, all operators correspond to phase index 0.

◼ See also: isospinx, isospiny, isospinz,  manyspin.

Further examples

Load sneg and declared c and d to be fermionic operators

<< sneg`sneg`;
snegfermionoperators[c, d];

{(Subscript[I, x]), (Subscript[I, y]), (Subscript[I, z]), II} = 
      manyisospin[{c[], d[]}]
komutator[(Subscript[I, x]), (Subscript[I, y])] == I (Subscript[I, z]) // 
      ExpandAll
komutator[(Subscript[I, y]), (Subscript[I, z])] == I (Subscript[I, x]) // 
      ExpandAll
komutator[(Subscript[I, z]), (Subscript[I, x])] == I (Subscript[I, y]) // 
      ExpandAll
komutator[II, (Subscript[I, x])] == 0 // ExpandAll
komutator[II, (Subscript[I, y])] == 0 // ExpandAll
komutator[II, (Subscript[I, z])] == 0 // ExpandAll

Check that the total isospin operators commute with the total spin operators

{(Subscript[S, x]), (Subscript[S, y]), (Subscript[S, z]), SS} = 
      manyspin[{c[], d[]}]
Outer[komutator, {(Subscript[S, x]), (Subscript[S, y]), (Subscript[S, z])}, {(Subscript[I, x]), (Subscript[I, y]), (Subscript[I, z])}] // 
      Expand