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Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program

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arxiv 1004.3417 v3 pith:IHCKDRXN submitted 2010-04-20 hep-th

Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program

Bo Feng , Rijun Huang , Yin Jia This is my paper
classification hep-th
keywords relationon-shellamplitudegaugeprogramproofrecursions-matrix
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Using only the Britto-Cachazo-Feng-Witten(BCFW) on-shell recursion relation we prove color-order reversed relation, $U(1)$-decoupling relation, Kleiss-Kuijf(KK) relation and Bern-Carrasco-Johansson(BCJ) relation for color-ordered gauge amplitude in the framework of S-matrix program without relying on Lagrangian description. Our derivation is the first pure field theory proof of the new discovered BCJ identity, which substantially reduces the color ordered basis from $(n-2)!$ to $(n-3)!$. Our proof gives also its physical interpretation as the mysterious bonus relation with ${1\over z^2}$ behavior under suitable on-shell deformation for no adjacent pair.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Color-factor symmetry using perturbiner methods for tree-level amplitudes of Yang-Mills theory coupled to matter

    hep-th 2026-07 accept novelty 6.0

    Perturbiner recursion proves color-factor symmetry (hence BCJ relations) for all tree-level YM+matter amplitudes with at least one gluon.

  2. Color-factor symmetry using perturbiner methods for tree-level amplitudes of Yang-Mills theory coupled to matter

    hep-th 2026-07 accept novelty 6.0

    A new perturbiner proof shows tree-level Yang-Mills amplitudes with any number of fundamental scalars or spinors and at least one gluon are invariant under color-factor shifts, yielding BCJ relations.

  3. Hidden Zeros and $2$-split via BCFW Recursion Relation

    hep-th 2025-04 unverdicted novelty 4.0

    Hidden zeros in NLSM amplitudes are proven via modified BCFW recursion, with 2-split holding only under careful current definition.