feynlag.groups.discrete.S3

class feynlag.groups.discrete.S3(name='S3')[source]

The permutation group S₃ with irreps '1', '1p', '2'.

Generators: a = 3-cycle, b = transposition. The 2-dimensional irrep uses the real orthogonal basis: ρ(a) = R(2π/3), ρ(b) = diag(1, -1).

Clebsch–Gordan for doublets x = (x₁,x₂), y = (y₁,y₂) in this basis (2⊗2 = 1 ⊕ 1’ ⊕ 2), available via doublet_product().

__init__(name='S3')[source]

Methods

__init__([name])

assign(irrep, *multiplet)

Assign a field multiplet to an irrep.

components()

All component symbols across every assigned multiplet.

doublet_product(x, y)

CG decomposition of 2 ⊗ 2 in the real orthogonal basis.

fermion_generator_data()

Per-generator transform data for fermion multiplets.

generator_maps()

Substitution dicts, one per group generator, over all assignments.

rep_dim(irrep)

Attributes

irreps

assignments

list of (irrep_label, tuple_of_multiplet_members)