feynlag.groups.gauge

Gauge groups with explicit generator matrices.

• U1: representation label = the charge (a Rational/number).

• SUN: any SU(N); representations are built dynamically in the Gelfand–Tsetlin basis (see feynlag.groups.sun). Labels may be an integer dimension (1 → trivial, N → fundamental, N²−1 → adjoint, other ints resolved by the Weyl dimension formula), a conjugate label (negative int −d or string "dbar"), or an explicit Dynkin tuple (a_1, …, a_{N−1}). Conjugate reps have T̄^a = −(T^a)^*.

• SU2, SU3: thin subclasses of SUN kept for the familiar names and legacy dimension labels (SU2: 1/2/3, SU3: 1/3/8); their generators are byte-identical to the historic σ/2 / λ/2 / −i f.

Every representation of a group shares the fundamental’s structure constants f^{abc}, so [T^a,T^b] = i f^{abc} T^c holds across reps automatically — the property the covariant derivative and Yang–Mills self-couplings rely on. Adjoint generators are (T^a)_{bc} = −i f^{abc}.

Classes

SU2(name[, coupling])	SU(2); legacy labels 1 (singlet), 2 (fundamental), 3 (adjoint).
SU3(name[, coupling])	SU(3); legacy labels 1 (singlet), 3 (fundamental), 8 (adjoint).
SUN(N, name[, coupling])	SU(N) with representations built dynamically for any N and any irrep.
U1(name[, coupling])	Abelian U(1) group; a field's representation IS its charge.