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Note that the finite transformation of: $$W^a_\mu \to W^a_\mu + \frac{1}{g} \partial_\mu \theta^a + \epsilon^{abc} \theta^b W^c_\mu$$ is: $$W^a_\mu t^a \to g W_\mu^a t^a g^{-1} + \frac{i}{g} \partial_\mu g \tag{1}$$ where: $$g = \exp(-i \theta^a t^a) \;\;\; \text{and} \;\;\; [t^a,t^b] = i \epsilon^{abc} t^c$$ Thus, the first term on the right-hand ...

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Maybe I've figure out something about that. QCD is an asymptotically free theory, so while for the high energy regime, consider the perturbative method, expanding around $g=0$, is perfectly consistent, for the low energy scales this approach becomes useless. An attempt to manage this problem, is to consider an expansion in terms of the parameter ...

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On one hand, by including the Lautrup-Nakanishi field $B^a$, we have an off-shell BRST formulation, i.e. we can prove the nilpotency of the BRST transformation without using the (Euler-Lagrange) equations of motion. On the other hand, for some applications, a simpler on-shell BRST formulation (where the Lautrup-Nakanishi field $B^a$ has been integrated ...

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I will try to avoid too many details. In case you want to learn more about these things I could suggest this reference: http://arxiv.org/pdf/1308.1697.pdf and from it you can find more references. First of all, the Parke-Taylor formulas is about the so called MHV (Maximal Helicity Violating) Amplitudes and with the use of the spinor-helicity formalism they ...

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