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High Energy, Nuclear, Particle Physics
Four Bosons vertex related to gauge symmetry
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[QUOTE="nrqed, post: 5626081, member: 15416"] I don't want to sound like I am nitpicking, but strictly speaking this interaction is not present in what is typically considered to be the QED Lagrangian. I know that it appears in the Euler-Heisenberg lagrangian and it must be present of we think of QED as an effective field theory (as it must be) but if we talk about QED being the theory described in most textbooks, there is no tree level four photon interaction. To the OP: there is no [B]tree level four photon interaction[/B] in QED but of course, there are higher order (loop) diagrams that do produce four photon interactions. the reason there is no tree level four photon interactions but there is a tree level four gluon vertex is indeed because of the difference between U(1) and SU(N), the former is abelian while the later are non abelian. The difference appears through the definition of [itex] F_{\mu\nu} [/itex]. The key point is that it contains the commutator [itex] [A_\mu, A_\nu ][/itex] For an abelian group like U(1), this vanishes. For SU(N), it does not. Because of this the term [itex] F_{\mu \nu} F^{\mu \nu} [/itex] will contain an explicit term of the form [itex] A_\mu A_\nu A^\mu A^\nu [/itex] for SU(N). [/QUOTE]
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Four Bosons vertex related to gauge symmetry
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