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.
Questions tagged [1pi-effective-action]
169 questions
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Difference between 1PI effective action and Wilsonian effective action?
What is the simplest way to describe the difference between these two concepts, that often go by the same name?
Newman
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In what sense is the proper/effective action $\Gamma[\phi_c]$ a quantum-corrected classical action $S[\phi]$?
There is a difference between the classical field $\phi(x)$ (which appears in the classical action $S[\phi]$) and the quantity $\phi_c$ defined as $$\phi_c(x)\equiv\langle 0|\hat{\phi}(x)|0\rangle_J$$ which appears in the effective action. Even…
SRS
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Self-energy, 1PI, and tadpoles
I'm having a hard time reconciling the following discrepancy:
Recall that in passing to the effective action via a Legendre transformation, we interpret the effective action $\Gamma[\phi_c]$ to be the generating functional of 1-particle irreducible…
QuantumDot
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Proof that the effective/proper action is the generating functional of one-particle-irreducible (1PI) correlation functions
In all text book and lecture notes that I have found, they write down the general statement
\begin{equation}
\frac{\delta^n\Gamma[\phi_{\rm cl}]}{\delta\phi_{\rm cl}(x_1)\ldots\delta\phi_{\rm cl}(x_n)}~=~-i\langle…
dixi
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Defining quantum effective/proper action (Legendre transformation), existence of inverse (field-source)?
Given a Quantum field theory, for a scalar field $\phi$ with generic action $S[\phi]$, we have the generating functional $$Z[J] = e^{iW[J]} =
\frac{\int \mathcal{D}\phi e^{i(S[\phi]+\int d^4x J(x)\phi(x))}}
{\int \mathcal{D}\phi e^{iS[\phi]}}.$$…
Thomas
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How to perform a derivative of a functional determinant?
Let us consider a functional determinant
$$\det G^{-1}(x,y;g_{\mu\nu})$$
where the operator $G^{-1}(x,y;g_{\mu\nu})$ reads
$$G^{-1}(x,y;g_{\mu\nu})=\delta^{(4)}(x-y)\sqrt{-g(y)}\left(g^{\mu\nu}(y)\nabla^{(y)}_\mu\nabla^{(y)}_\nu+m^2\right).$$
Such…
Wein Eld
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Probabilistic Intuition behind connected correlations and 1PI vertex function
In the context of statistical field or quantum field theory, one encounters so called generating function(al) for connected correlations, aka the following function(al):
$$ W(J) = \ln (Z(J))$$
$$ Z(J) = \int \mathcal{D} \phi e^{-S[\phi]}$$
From a…
physicsdude
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Understand "Quantum effective action" in Weinberg's book "The quantum theory of fields"
In Weinberg's book "The Quantum theory of fields", Chapter 16 section 1: The Quantum Effective action. There is an equation (16.1.17), and several lines of explanation, please see the Images.
The Equation is used to calculate the effective action…
user35289
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2 answers
How to correctly understand these "1-particle-irreducible insertions"?
In QED, when dealing with the vacuum polarization and the photon propagator, some authors like Peskin & Schroeder introduce the so-called "1-particle irreducible" diagrams. These are defined as:
Let us define a one-particle irreducible (1PI)…
Gold
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13
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Coleman-Weinberg potential: resum at 2 loops?
Say we want to compute the Coleman-Weinberg potential at 2 loops.
The general strategy as we know is to expand the field $\phi$ around some background classical field $\phi \rightarrow \phi_b + \phi$, and do a path integral over the quantum part of…
zzz
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4 answers
Mass Renormalization: Geometric Series of One-Particle Irreducible Diagrams
Pretty much everywhere I look it is stated that the full two point Green function (let's say for the Klein-Gordon field) is a geometric series in the one particle irreducible diagrams, ie. in momentum space,
$$G(k) =…
JLA
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11
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Proof of renormalizability based on analyzing the symmetry of effective action: isn't regulator also important?
In QFT Vol2 written by Weinberg (Chap 16-17), or very much similarly in Adel Bilal's notes (Chap 7), a powerful way of proving renormalizability is presented: Analyze the symmetries of the quantum effective action (QEA), and since QEA generates all…
Jia Yiyang
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10
votes
1 answer
Perturbation expansion of effective action
Chapter 11.4 of Peskin & Schroeder's book discusses the computation of 1PI effective action, but I don't understand some details of derivation.
The book first splits the Lagrangian into normal ones and counterterms.
$$L=L_1+\delta…
Eric Yang
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votes
1 answer
1PI effective potential vs self-energy
Consider the following Lagrangian describing the interaction between a massless field $\phi$ and a massive field $\psi$:
$$
{\scr L} = \frac12(\partial\phi)^2 + \frac12 (\partial\psi)^2(1 + f(\phi/M)) - \frac12m^2\psi^2.\tag{1}
$$
The interaction…
Guy
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Anomaly is due to the noninvariance of the path-integral under a symmetry. Is the noninvariance reflected on 1PI effective action?
When a symmetry is anomalous, the path integral $Z=\int\mathcal{D}\phi e^{iS[\phi]}$ is not invariant under that group of symmetry transformations $G$. This is because though the classical action $S[\phi]$ is invariant the measure may not be…
SRS
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