Questions tagged [1pi-effective-action]
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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2PI Effective Action from Double Legendre Transformation
This answer (https://physics.stackexchange.com/q/348673) provides good intuition for why Legendre transformation induces 1-particle irreducible graphs:
It mainly tries to convey the idea that the ...
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Goldstone theorem for classical and quantum potential
Consider a quantum theory $$\mathcal{L}(\phi^a) = \mathcal{L_{kin}}(\phi^a)-V(\phi^a),\tag{11.10}$$ depending on any type of fields $\phi^a$.
The VEV of this theory are constant fields $\phi_0^a$ such ...
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Relation between Dyson equation, Kadanoff-Baym equations and 2PI formalism
I am learning the framework of non-equilibrium field theory. Probably this is clear enough to an expert, but the expansive number of formalism, methods, and frameworks is confusing for a beginner.
I ...
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What's the minima of the quantum effective action?
Consider the vacuum expectation value of a (for simplicity scalar) field $\phi$, we know that its vacuum expectation value can be expressed as
$$\langle\phi\rangle=\frac{1}{\mathcal{Z}}∫\mathcal{D}\...
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Missing counterterms in $\phi^3$ + $\phi^4$ theory in 1PI effective action
I hope I'm just overlooking something. The Lagrangian is as follows:
$$\mathcal{L}=\frac{1}{2}(\partial_\mu \phi)^2-(\frac{1}{2}m^2\phi^2+\frac{1}{3!}g\phi^3+\frac{1}{4!}\lambda\phi^4)$$
and I just ...
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What are exactly the loop correction to the potential? [duplicate]
I am struggling with the concept of quantum effective action, but first recall the definition : given a Wilsonian effective action $W[J]$ of our theory, the quantum effective action is just
$$\Gamma[\...
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Understanding $W^{(n)}$, $\Gamma^{(n)}$, and $\Sigma$ in Feynman diagrams
In quantum field theory (specifically $\phi^4$ theory), $W$ is the sum of all connected Feynman diagrams and the effective action $\Gamma$ is the sum of all 1PI Feynman diagrams. They are related by a ...
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One-loop effective potentials and Schwinger's parametrisation
I was reading this paper where they calculate the effective potential of a scalar field $\phi$, which is (without any justification)
$$
V_{eff} (\phi) = \dfrac{1}{2} \sum_I (-1)^{F_i} \int \dfrac{d^4 ...
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Quantum effective action for Yang-Mills theories
During a course I came across a formula for the quantum effective action of a Yang-Mills theory in euclidean space and it appears like this (some indices may be dropped but I hope that won't be a ...
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In QFT, is the effective potential at tree-level always the same as the potential? Why?
If I have a simple scalar theory
$$ \mathcal{L}(\phi) = \frac{1}{2} (\partial_\mu \phi)^2 - V(\phi), $$
the effective potential $V_{eff}$, derived from $Z\rightarrow W \rightarrow \Gamma \rightarrow ...
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Renormalization conditions and proper vertices at tree level
I'm trying to understand a statement of my teacher of TQFT: he said that when expanding the effective action in terms of proper vertices, we can choose a new theory with only tree diagrams in order to ...
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Generating functional for fields with non-zero expectation value
When doing QFT or statistical field theory of, say $N$ scalar fields $\varphi_i$, we consider the the generating functional
$$
W[J] = - \ln Z[J], \quad Z[J] = \int \mathcal D \varphi \, e^{-S[\varphi] ...
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Evaluation of functional derivative of effective action
I'm trying to understand a calculation in appendix A of this paper https://arxiv.org/abs/2204.04197, however I don't understand how they end up with equation (125) and I think I am going wrong in the ...
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1PI effective action and Action generated through Hubbard-Stratonovich transformation
In standard lectures on advanced QFT one learnt that performing Legendre transformation leads to effective actions generating one-particle-irreducible (1PI) diagrams, which is encoded by Schwinger-...
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Clarification in Weinberg's 2nd QFT book about 1PI quantum effective action and effective potential
I'm going over the quantum effective action section in Weinberg second QFT book, I understood his derivation and reasoning up to the equation:
$$iW[J]=\int_{\substack{Connected\\trees}}\left[\mathcal{...
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