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3

You have stumbled upon the spinor helicity formalism. The idea is as follows. Massless spinors have many useful relationships among them that we can use. Thus instead of using the polarization vector, $\epsilon_\mu$ or massive spinors lets just map these objects into massless spinors and then use the convenient relationships between them to simplify ...

2

No, the gauge current need not be gauge invariant, since it carries a group index in non-abelian theories. You should recall that both sides of the Yang-Mills equation (and therefore the current itself) are Lie-algebra valued and therefore transform in the adjoint representation. Not even the field strength $F^a_{\mu\nu}$ is gauge invariant, but transforms ...

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I ended up spending an hour or so wading through the papers, so here's my main conculsion from that: No, I don't think the critique of the papers is wrong; Nor do I think that the basic algebraic arguments in the three papers addressed by the critique are wrong either. The authors describe a particular "decomposition" of the electromagnetic fields into a ...

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