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Physics
High Energy, Nuclear, Particle Physics
Superficial degree of divergence for scalar theories
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[QUOTE="nrqed, post: 5463998, member: 15416"] Hi again! Well, it is just a question of terminology. The way I see it is that we are considering one theory (because we are dealing with a single lagrangian) but this theory may contain an infinite number of terms. Even if there is an infinite number of terms it is still one theory. Yes, we can write this. Not necessarily! One can also have ##\phi^4,\phi^5 \ldots ## terms! The theory will be nonrenormalizable but it is still perfectly well defined as an effective field theory Watch out. This box diagram has four external lines. Therefore ##[g_E]## is the dimension of the coefficient of an ##\phi^4## interaction would have (note that it does not matter if there is such an interaction in the Lagrangian or not, ##[g_E]## is the dimension of the coefficient of such an interaction if it was present) and for a ##\phi^4## interaction in 6 dimensions, the coefficient would have dimension -2. So for your diagram, ##[g_E]=-2## and therefore D=-2. [/QUOTE]
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High Energy, Nuclear, Particle Physics
Superficial degree of divergence for scalar theories
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