TFPT scientific source excerpt
Original repository path: verification/v1002_spin10_mirror_projector.py
Original file SHA-256: 84f7cd7987887ee071d7e05872285ab274ae329f6bcfa693be69bb52add19a4c
Inclusive original lines: 123-152
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000123 | def positive_weyl_generators():
000124 |     gammas = gamma_matrices_10d()
000125 |     clifford_deviation = max(
000126 |         np.max(
000127 |             np.abs(
000128 |                 gammas[a] @ gammas[b]
000129 |                 + gammas[b] @ gammas[a]
000130 |                 - (
000131 |                     2.0 * np.eye(32, dtype=complex)
000132 |                     if a == b
000133 |                     else np.zeros((32, 32), dtype=complex)
000134 |                 )
000135 |             )
000136 |         )
000137 |         for a in range(10)
000138 |         for b in range(10)
000139 |     )
000140 |     gamma_product = np.eye(32, dtype=complex)
000141 |     for gamma in gammas:
000142 |         gamma_product = gamma_product @ gamma
000143 |     chirality = ((-1j) ** 5) * gamma_product
000144 |     positive = np.flatnonzero(np.real(np.diag(chirality)) > 0.5)
000145 |     if len(positive) != SPIN10_MODES or clifford_deviation > TOL:
000146 |         raise RuntimeError("failed to reconstruct the positive Weyl module")
000147 |     pairs = list(itertools.combinations(range(10), 2))
000148 |     generators = [
000149 |         (0.5j * gammas[a] @ gammas[b])[np.ix_(positive, positive)]
000150 |         for a, b in pairs
000151 |     ]
000152 |     return generators, pairs