nambu

◼ nambu[c, i] returns the Nambu spinor components corresponding to a fermionic operator c. The phase in the spin-down component of the spinor is (((-1))^i).

◼ Operator c must be expressed in the stripped form, i.e. a form which excludes the first index (creation/annihilation) and the last index (spin).

◼ The default value for i is 0.

◼ The spin up version of the Nambu spinor is returned.

◼ nambu is used in the construction of the isospin operators.

◼ See also: isospinxyz.

Further examples

Load sneg and declare c to be a fermionic operator

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

Nambu spinor ξ

ξ = nambu[c[]];
MatrixForm[ξ]

The first component of ξ has (Subscript[I, z]) = 1/2,  (Subscript[S, z]) = 1/2, the second component of ξ has (Subscript[I, z]) = -1/2,  (Subscript[S, z]) = 1/2.  The Nambu spinor is a spherical tensor operator with respect both to spin SU(2) group and to isospin SU(2) group.

sz = spinz[c[]];
komutator[sz, ξ] // Expand
% == 1/2  ξ
iz = isospinz[c[]];
komutator[iz, ξ] // Expand
% == {1/2, -1/2} ξ

Note that the sign of the isospin down component of the Nambu spinor depends on a phase index.

nambu[c[], 0]
nambu[c[], 1]