TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/canonical-seam-fermionization-20261025/NEUTRAL-NET-AND-DEFECT.txt
Original file SHA-256: 8693dfceba1cd03631bbbcd476029b89734447b6184fda9f766870a2fad750b2
Inclusive original lines: 85-109
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000085 | -----------------------------------------
000086 | 
000087 | Use
000088 | 
000089 |   tau_t(c(f))=c(exp(i t B_a)f).
000090 | 
000091 | The one-particle Ward relation is
000092 | 
000093 |   exp(i t B_a) u exp(-i t B_a)=exp(i t)u.               (6)
000094 | 
000095 | Since c(f) is anti-linear in f,
000096 | 
000097 |   tau_t Ad(W1)(c(f))
000098 |     =exp(-i t) Ad(W1) tau_t(c(f)).                      (7)
000099 | 
000100 | Let gamma_t be the gauge action gamma_t(c(f))=exp(-it)c(f). Then on the
000101 | full field net
000102 | 
000103 |   tau_t Ad(W1)=gamma_t Ad(W1) tau_t.                    (8)
000104 | 
000105 | On A_0, gamma_t is the identity, and consequently
000106 | 
000107 |   tau_t Ad(W1)|A_0=Ad(W1) tau_t|A_0.                    (9)
000108 | 
000109 | This proves the claimed time commutation on the neutral observer net. It is