TFPT scientific source excerpt
Original repository path: verification/v252_full_finite_triple.py
Original file SHA-256: 820254440e178430422e50605067775656236602996307f67c9e69124ba5d163
Inclusive original lines: 72-168
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000072 | def build_index():
000073 |     P = []
000074 |     for g in range(NG):
000075 |         for (name, ch, c) in GEN_FIELDS:
000076 |             P.append((name, ch, c, g))
000077 |     idx = {f: i for i, f in enumerate(P)}
000078 |     return P, idx
000079 | 
000080 | 
000081 | P, IDX = build_index()
000082 | NP = len(P)                 # 48 particle states
000083 | NH = 2 * NP                 # 96 full
000084 | 
000085 | 
000086 | def dirac_block(Yu, Yd, Ye, Ynu):
000087 |     """particle 48x48 Yukawa block S (Hermitian): L<->R per field/colour."""
000088 |     S = np.zeros((NP, NP), complex)
000089 |     table = {"u": Yu, "d": Yd, "e": Ye, "nu": Ynu}
000090 |     for (name, ch, c, g) in P:
000091 |         if ch != "L":
000092 |             continue
000093 |         Y = table[name]
000094 |         for gj in range(NG):
000095 |             i = IDX[(name, "L", c, g)]
000096 |             j = IDX[(name, "R", c, gj)]
000097 |             S[i, j] = Y[g, gj]
000098 |             S[j, i] = np.conjugate(Y[g, gj])
000099 |     return S
000100 | 
000101 | 
000102 | def full_D(Yu, Yd, Ye, Ynu, MR):
000103 |     """D_F = [[S, T],[T^dag, conj S]] ; T = Majorana on nu_R (particle<->antiparticle)."""
000104 |     S = dirac_block(Yu, Yd, Ye, Ynu)
000105 |     T = np.zeros((NP, NP), complex)
000106 |     for g in range(NG):
000107 |         for gj in range(NG):
000108 |             i = IDX[("nu", "R", 0, g)]
000109 |             j = IDX[("nu", "R", 0, gj)]
000110 |             T[i, j] = MR[g, gj]
000111 |     D = np.zeros((NH, NH), complex)
000112 |     D[:NP, :NP] = S
000113 |     D[NP:, NP:] = np.conjugate(S)
000114 |     D[:NP, NP:] = T
000115 |     D[NP:, :NP] = T.conj().T
000116 |     return D
000117 | 
000118 | 
000119 | def grading():
000120 |     gp = np.array([1.0 if ch == "L" else -1.0 for (_, ch, _, _) in P])
000121 |     return np.diag(np.concatenate([gp, -gp]))      # antiparticles: opposite chirality
000122 | 
000123 | 
000124 | def Kswap():
000125 |     K = np.zeros((NH, NH))
000126 |     K[:NP, NP:] = np.eye(NP)
000127 |     K[NP:, :NP] = np.eye(NP)
000128 |     return K
000129 | 
000130 | 
000131 | def Japply(v, K):
000132 |     return K @ np.conjugate(v)                       # antilinear J = swap . conj
000133 | 
000134 | 
000135 | def quaternion(a, b):
000136 |     return np.array([[a, b], [-np.conjugate(b), np.conjugate(a)]], complex)
000137 | 
000138 | 
000139 | def rep(lam, q, m):
000140 |     """pi(a), a=(lam in C, q in H (2x2), m in M_3(C)).  Bimodule split:
000141 |     particles -> (lam,q) colour-trivial ; antiparticles -> (lam,m) weak-trivial."""
000142 |     pi = np.zeros((NH, NH), complex)
000143 |     # ---- particle block: weak/hypercharge action, identity on colour ----
000144 |     for g in range(NG):
000145 |         # lepton doublet (nu_L,e_L) <- q ;  nu_R<-lam, e_R<-conj(lam)
000146 |         nl, el = IDX[("nu", "L", 0, g)], IDX[("e", "L", 0, g)]
000147 |         pi[nl, nl], pi[nl, el] = q[0, 0], q[0, 1]
000148 |         pi[el, nl], pi[el, el] = q[1, 0], q[1, 1]
000149 |         pi[IDX[("nu", "R", 0, g)], IDX[("nu", "R", 0, g)]] = lam
000150 |         pi[IDX[("e", "R", 0, g)], IDX[("e", "R", 0, g)]] = np.conjugate(lam)
000151 |         for c in range(3):
000152 |             ul, dl = IDX[("u", "L", c, g)], IDX[("d", "L", c, g)]
000153 |             pi[ul, ul], pi[ul, dl] = q[0, 0], q[0, 1]
000154 |             pi[dl, ul], pi[dl, dl] = q[1, 0], q[1, 1]
000155 |             pi[IDX[("u", "R", c, g)], IDX[("u", "R", c, g)]] = lam
000156 |             pi[IDX[("d", "R", c, g)], IDX[("d", "R", c, g)]] = np.conjugate(lam)
000157 |     # ---- antiparticle block: colour action m on quarks, lam on leptons ----
000158 |     off = NP
000159 |     for g in range(NG):
000160 |         for (name, ch, c, gg) in [f for f in P if f[3] == g]:
000161 |             i = off + IDX[(name, ch, c, g)]
000162 |             if name in ("nu", "e"):
000163 |                 pi[i, i] = lam
000164 |             else:                                    # quark: colour matrix m
000165 |                 for c2 in range(3):
000166 |                     j = off + IDX[(name, ch, c2, g)]
000167 |                     pi[i, j] = m[c, c2]
000168 |     return pi