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36 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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55 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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41 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} ...
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0answers
41 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
25 views

Meaning of negative effective range

In a case of a square-well potential the effective range and the scattering lenght depends on the characteristic parameter of the potential (see the explicit formula here, eq. 25a,25b ) and the plot ...
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0answers
28 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} ...
7
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1answer
235 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
121 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
58 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} ...
5
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1answer
357 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
320 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
300 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
211 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
68 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
349 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
99 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
191 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 ...
13
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1answer
179 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 ...
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1answer
303 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, it was discovered that the theory had some very bad properties. It took twenty years to discover that certain naturally arising infinities could ...
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2answers
764 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 ...