Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I'm reading Appendix 1 of Section N2 (Gluon Scattering) in "Quantum Field Theory in a Nutshell" by Anthony Zee. The generators for SU(N) have the usual algebra

[tex][T^a, T^b] = i \epsilon^{a b c}T^c[/tex]

Suppose we adopt the following normalization

[tex]\text{tr}(T^a T^b) = \frac{1}{2}\delta^{a b}[/tex]

Then, we have

[tex]\text{tr}([T^a, T^b]T^c) = \text{tr}(i f^{a b e} T^{e} T^{c}) = i f^{a b e}\text{tr}(T^e T^c) = \frac{i f^{a b e} \delta^{e c}}{2} = \frac{i f ^{a b c}}{2}[/tex]

so that

[tex]f^{a b c} = - 2 i \text{tr}([T^a, T^b]T^c)[/tex]

Also,

[tex]\text{tr}([T^a, T^b][T^c, T^d]) = \text{tr}(i f^{a b \alpha} T^{\alpha} i f ^{c d \beta} T^{\beta}) = -f^{a b \alpha} f^{c d \beta}\text{tr}(T^\alpha T^\beta) = -\frac{1}{2}f^{a b e} f^{c d e}[/tex]

which implies that

[tex]f^{a b e} f^{c d e} = -2 \text{tr}([T^a, T^b][T^c, T^d])[/tex]

However, the author explicitly states that

[tex]f^{a b e} f^{c d e} = -4 \text{tr}([T^a, T^b][T^c, T^d])[/tex]

I don't get this additional factor of 2. What am I missing? Is there an error somewhere?

Thanks in advance!

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Gluon Scattering - Colored Feynman Rules for Yang Mills Theory

Loading...

Similar Threads - Gluon Scattering Colored | Date |
---|---|

I Why is there an arrow mediating a process in a Feynman diagram? | Mar 15, 2018 |

I Gluon Field Fluctuations | Dec 28, 2016 |

Is there a blue-anti blue gluon? | Aug 26, 2014 |

Extracting Gluons from Atoms | May 26, 2013 |

Quark-gluon plasma | Sep 26, 2012 |

**Physics Forums - The Fusion of Science and Community**