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1answer
54 views

How to calculate the effective action in general?

Considering the scalar field, we have the effective action $$\tag 1 \Gamma[\phi_{cl}]=\int ...
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161 views

What is the effective (quantum) lagrangian of a fermion field for fixed electromagnetic field?

... or, put it another way, what are the loop corrections to the dirac equation in the presence of a fixed (external) electromagnetic field?. Background Let $\mathcal ...
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1answer
38 views

What does “n-particle reducible” mean?

I am reading Ramond and in page 112 he says "In $\lambda \phi^{4}$ theory, diagrams can be at most three-particle reducible". My question: whether the individual Feynman Diagrams are treated as ...
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1answer
87 views

Resources for 2 Particle Irreducible (2PI) or Cornwall-Jackiw-Tomboulis (CJT) formalism

I'am currently learning the 2 particle irreducible (2PI) or Cornwall-Jackiw-Tomboulis (CJT) formalism. Does anybody know a textbook or a review that treats this subject? As far I only found the ...
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1answer
59 views

What are the 1PI correlations functions?

This question may be a little strange, but I'm currently going through my lecture notes and in the construction of the 1PI effective action there is a constant reference to 1PI correlation functions. ...
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0answers
45 views

How can the VEV of a field be a function of spacetime?

Often in the discussion of effective action and effective potential (say, in the context of $\phi^4-$theory )the one-point function in presence of source is defined as \begin{equation} \frac{\delta ...
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1answer
78 views

One-point function and vacuum expectation value in $\phi^4$-theory

Why is it that the one-point function in the $\phi^4-$theory, for example calculated from the generating functional, always gives zero value in absence of external source i.e., $J=0$? If there is ...
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2answers
60 views

Does the connected Green's function's decomposition into 1PI-s have connected contributions, or can it be written exclusively using 1PI-s?

While reading this article by Abbot on the background field method, in Fig 5. on page 38 (page 6 in the pdf file), we can see the relation between connected contributions to the two point function and ...
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1answer
94 views

Loopwise expansion of effective action $\Gamma[\phi]$

My question is about the loopwise expansion of the effective action $\Gamma(\varphi)$ up to 1-loop contributions. I've understood well the results for both $Z[J]$ and $W[J]$ functionals loopwise ...
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0answers
187 views

One loop effective potential of Standard Model

The one loop Coleman-Weinberg contribution of a scalar field to the effective potential (in MSbar scheme) is: \begin{equation} const. \times m^4(\phi_c) \left( log \left( ...
3
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0answers
291 views

Effective field theories and gauge anomalies cancellation

Lets assume some theory which concludes sets of generations of fermions (lets call them $A$ and $B$). Fermions $A$ have some gauge group $G_{A}$ (for example, SM), while fermions $B$ are charged under ...
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52 views

Weinberg's spontaneous broken symmetries

Steven Weinberg in his second volume of QFT's book (in section about spontaneously broken symmetries, in subsection about Goldstone bosons) writes following: if we have linear transformation of ...
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0answers
55 views

Does graviton loops affect the seperately covariant conservation of energy momentum of two noninteracting sectors of matter

Consider the action $$\int \sqrt{-g}\left[R[g]+\mathcal{L}_{m1}(g,\psi_1)+\mathcal{L}_{m2}(g,\psi_2)\right]$$ Classically we have $$\nabla^\mu T^1{}_{\mu\nu}=0,\,\,\,\,\nabla^\mu T^2{}_{\mu\nu}=0$$ ...
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0answers
85 views

Is it possible to derive the effective potential of a given theory by only using the RGE equations?

I know that it is possible to derive the RGE equations from the effective potential by requiring that the first derivative with respect to the renormalization scale $\mu$ vanishes: $$ ...
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0answers
136 views

Proof that the effective 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} ...
2
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1answer
70 views

Why is the effective action $\Gamma[\phi_c] \propto -(VT)$ (spacetime volume)?

I'm asking about equation $(11.50)$ in Peskin and Schroeder where they state that the effective action evaluated at the classical field is given by $$\tag{11.50}\Gamma[\phi_c] = -(VT)\cdot ...
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0answers
45 views

Nonlocal interaction effects on bose-einstein condensates

I'm studying an interacting bose-einstein condensate using the energy functional proposed in this paper K. Huang, C.N. Yang, Phys. Rev. 105 $$ E\left[\phi\right] = \int d^3\vec{r} ...
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1answer
527 views

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 + ...
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2answers
312 views

Defining quantum effective 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 ...
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0answers
78 views

Energy interpretation of 1PI effective potential in Weinberg 16.3: is adiabatic turning on the current necessary?

In section 16.3 of Weinberg, he interprets the 1PI effective potential as the minimum of expectation value of the energy density under some constraint. The essential argument is \begin{equation} ...
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1answer
765 views

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 a equation (16.1.17), and several lines of explanation, please see the Images. The ...
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1answer
632 views

Connected and strongly connected Feynman diagrams

Recently I read, that only connected Feynman diagrams give contribution of nonzero values into the scattering amplitude. Why it is so and what is the physical sense of connected diagrams (due to ...
7
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1answer
392 views

How to understand the Lagrangian of the standard model, effective or “fundamental”

I have a question about understanding the Lagrangian of standard model, should we view it as a "fundamental" or effective theory? The "fundamental" theory here means the theory with physical cutoff ...
3
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1answer
292 views

Does effective theory have the same meaning in particle and condensed matter physics

I have a naive question about the meaning of effective theory in particle physics and condensed matter physics. In particle physics, from what I know, the effective theory comes from the Wilsonian ...
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0answers
74 views

Does the ensemble of effective Lagrangians in the String theory landscape mostly include gauge theories?

String theory false vacua can be described by effective Lagrangians at low energy. Is there generally a correspondence between these effective Lagrangians and SU(N) gauge theories? Or do the effective ...
5
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1answer
467 views

Higher dimension operator in free Dirac Lagrangian

When discussing higher dimensional operators in a theory with fermions, why do I never see anyone ever talk about the dimension five operator $\partial_\mu\bar\psi\partial^\mu\psi$? How does the ...
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0answers
124 views

Wilsonian vs 1PI

As a follow up to Difference between 1PI effective action and Wilsonian effective action, where can I find pedagogical material that highlights the similarities and differences between the 1PI and ...
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2answers
2k views

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 ...
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0answers
313 views

How to show the oblique parameters S, T, and U are coefficients of d=6 operators

In Morii, Lim, Mukherjee, The Physics of the Standard Model and Beyond. 2004, ch. 8, they claim that the Peskin–Takeuchi oblique parameters S, T and U are in fact Wilson coefficients of certain ...
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1answer
1k views

Difference between 1PI effective action and Wilsonian effective action?

What is the simplest ay to describe the difference between these two concepts, that often go by the same name?
14
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1answer
229 views

6d Massive Gravity

Massive gravity (with a Fierz-Pauli mass) in 4 dimensions is very well-studied, involving exotic phenomena like the vDVZ discontinuity and the Vainshtein effect that all have an elegant and physically ...
1
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1answer
344 views

Energy, power and action

Through unit analysis, one can identify the following relationship linking energy, action and power: $energy^2 = action \times power$ Alternatively, we rewrite this expression as: $power = ...
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3answers
2k views

A pedestrian explanation of Renormalization Groups - from QED to classical field theories

shortly after the invention of quantum electrodynamics, one discovered that the theory had some very bad properties. It took twenty years to discover that certain infinities could be overcome by a ...
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2answers
874 views

Steps for going from Polyakov action to low-energy effective action (SUGRA?) in String Theory

A lot of string-theory questions have been asked here. This one is, hopefully, different in that this inquiry is specific and the expected answer would be more mathematical than philosophical in ...