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An algebraic approach to BCJ numerators

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Abstract

One important discovery in recent years is that the total amplitude of gauge theory can be written as BCJ form where kinematic numerators satisfy Jacobi identity. Although the existence of such kinematic numerators is no doubt, the simple and explicit construction is still an important problem. As a small step, in this note we provide an algebraic approach to construct these kinematic numerators. Under our Feynman-diagram-like construction, the Jacobi identity is manifestly satisfied. The corresponding color ordered amplitudes satisfy off-shell KK-relation and off-shell BCJ relation similar to the color ordered scalar theory. Using our construction, the dual DDM form is also established.

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Authors and Affiliations

  1. Center of Mathematical Science, Zhejiang University, 38 Zheda Road, Hangzhou, 310027, P.R China

    Chih-Hao Fu & Bo Feng

  2. Department of Electrophysics, National Chiao Tung University, 1001 University Street, Hsinchu, Taiwan, R.O.C.

    Chih-Hao Fu

  3. Department of Physics and Center for Field Theory and Particle Physics, Fudan University, Shanghai, 200433, P.R China

    Yi-Jian Du

  4. Zhejiang Institute of Modern Physics, Zhejiang University, 38 Zheda Road, Hangzhou, 310027, P.R China

    Yi-Jian Du & Bo Feng

Authors
  1. Chih-Hao Fu
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  2. Yi-Jian Du
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  3. Bo Feng
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Correspondence to Chih-Hao Fu.

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ArXiv ePrint: 1212.6168

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Fu, CH., Du, YJ. & Feng, B. An algebraic approach to BCJ numerators. J. High Energ. Phys. 2013, 50 (2013). https://doi.org/10.1007/JHEP03(2013)050

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