Research proof index

The subgroup of gaugeGroup := SU(3) × SU(2) × U(1) which preserves every HiggsVec by the action of StandardModel.HiggsVec.rep is given by SU(3) × ℤ₆ where ℤ₆ is the subgroup of SU(2) × U(1) with elements (α^(-3) * I₂, α) where α is a sixth root of unity. -/ informal_lemma stability_group where deps := [``HiggsVec] tag := "6V2MO" /-! ## A.8...

The action of the full gauge group on a tensor product of basis elements, expanded as a sum over the columns of the SU(3) and SU(2) matrices.

The action of the full gauge group on a tensor product of basis elements, expanded as a sum over the columns of the SU(3) matrix.

The top-row of the standard parameterization is the cross product of the conjugate of the up and charm rows.

The standard parameterization forms a unitary matrix.

Single contraction. Contracting the last k of k+1 index pairs leaves one free pair σ, τ, with the factorial factor (4-1)(4-2)….