TFPT scientific source excerpt
Original repository path: verification/v252_full_finite_triple.py
Original file SHA-256: 820254440e178430422e50605067775656236602996307f67c9e69124ba5d163
Inclusive original lines: 139-168
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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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