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Physics

Questions tagged [1pi-effective-action]

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In quantum field theory, an effective action is a modified version of the action which takes into account quantum mechanical corrections. The effective action action is a generating functional of the one-particle-irreducible (1PI) diagrams, which are diagrams that cannot be broken into two disconnected diagrams by cutting an internal propagator.

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Page 370 (start of section 11.4) of Peskin and Schroeder claims that the VEV of a scalar field in the presence of an external source,$$\phi_\text{cl} \equiv \langle 0_J|\phi(x)|0_J\rangle,\tag{11.46}$...
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I'm following Cheng-Li to understand conventional renormalization of $-\lambda \phi^4 / 4!$ theory in 4D.ContextI understand that the only divergent 1PI Green's functions are $\Gamma^{(2)}(p^2)$ and ...
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Question. For which values of $N \geq 2$ and $D \geq 1$, such that $[\lambda] > 0$, $[\phi] < 0$, the scalar field theory $-\lambda \phi^N/N!$ in $D$ dimensions is renormalizable?Why the ...
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I'm studying the renormalizability of scalar quantum field theories. Take a theory with interaction lagrangian $-\lambda \phi^n / n!$.Question Is the condition $\Gamma^{(1)} = 0$ required for a ...
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I read through the paragraph of Srednicki and from what I understood the skeleton expansion can be summarized as:Consider a $\phi^3$ theory in 6 dimension:Compute the corrections to the 2-point ...
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I have a conformal theory where it is added 4 scalar fields to the SM. To compute the 1-loop correction mass we use the Coleman-Weinberg potential. The question is: if I use the Coleman-Weinberg ...
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We use the effective action to incorporate all quantum corrections, which in turn leads to the quantum-corrected equation of motion. Specifically, the effective action is given by:$$\Gamma_{\text{...
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I'm studying QFT, and we've recently introduced 1PI (one-particle-irreducible) diagrams, which are diagrams that remain connected even after cutting a single internal line.We also showed that only ...
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I've seen an explanation that every reducible diagram can be express as the multiplication of irreducible diagrams, however, if we simply multiply all irreducible diagrams together, wouldn't we be ...
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I am currently learning AQFT (advanced QFT) with the lecture notes of Osborn (I've had a course on QFT but this was not with the path integral formalism) and at some point he says the following$$\...
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In Higgs mass and vacuum stability in the Standard Model at NNLO, Eq. 52 gives the effective potential for the Higgs field as: $$\lambda_{\text{eff}}(h) = e^{4\Gamma(h)} \left\{ \lambda(h) + \frac{1}{(...
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In the paper Higgs Mass And Vacuum Instability in the Standard Model at NNLO, it is shown that the effective potential can be written in the form $V_{eff}(h) = \frac{\lambda_{eff}(h)}{4} h^4 $. Part ...
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I am trying to obtain an equation for the effective potential in orders of $\hbar$, but I am having serious difficulties in obtaining orders beyond the first. Several references go only as far as the ...
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I have a question regarding deriving the 1PI effective potential up to the 1-loop level of the $\phi^4$ renormalized theory. What I did is to renormalize the theory as follows:$$\mathcal{L}(\phi)=\...
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When looking at propagators (so expressions sandwiched between vacuum states) the first order in the exponential expansion of the $\phi^3$ theory vanishes because it gives 5 fields, viz$$\sim \langle ...

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