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Questions tagged [renormalization]

This tag is for questions which relates with the renormalization, an ensemble of techniques which serves to treat the infinities which appear in quantum field theory or statistical mechanics. Renormalization procedures are based on the requirement that certain physical quantities (such as the mass and charge of an electron) equal observed (experimental) values.

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Loop Effect of $\phi$ Propagator in $t$-channel of scalar $\phi^3$ theory [closed]

In Schwartz's QFT chapter 16, he calculates the loop effect (vaccum polarization) of $\phi$ propagator in $\phi^3$ theory, with the choice of Pauli-Villars regulator, the scattering amplitude would be ...
Ting-Kai Hsu's user avatar
1 vote
2 answers
72 views

Understanding Feynman Diagrams in Loop Corrections to the propagator $\phi ^3 $ theory [closed]

I found other posts talking about the same chapter in the same book, but none of them were exactly about what I am asking here. In Srednicki's chapter 14 (Loop corrections to the propagator), we are ...
Fernando Garcia Cortez's user avatar
2 votes
1 answer
110 views

What does it mean to "resum" the large logarithms?

I am struggling to understand the concept of resummation of large logarithms in QFT; from what I learnt so far the problem relies on the fact that if a full theory defined in the UV contains much ...
Filippo's user avatar
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0 answers
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Universality and continuous variation of critical exponent close to a tricritical point

A tricritical point is a point at which a second order transition line and a first order transition line merge. At equilibrium, this point can be described by a landau potential (see for example this ...
Syrocco's user avatar
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1 vote
1 answer
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Asymptotic Freedom QCD

I'm trying to understand the derivation of asymptotic freedom with the renormalisation group equations. I'm reading Taizo Muta's book on QCD. What I don't understand is how he obtains the last ...
Gogoman96 X's user avatar
4 votes
0 answers
105 views

Canonical commutation relation in QFT

The canonical commutation relation in QFT with say one (non-free) scalar real field $\phi$ is $$[\phi(\vec x,t),\dot \phi(\vec y,t)]=i\hbar\delta^{(3)}(\vec x-\vec y).$$ Is this equation satisfied by ...
MKO's user avatar
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Scaling equation for the external field H in an Ising like system [closed]

i want to show that the following relation is true for the external field H, starting from the scaling form of the free energy. It is an Ising like System close to a critical point with $M \geq 0$ and ...
Dorek's user avatar
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Conformal invariance and mass terms in QFT

We know that a physically sensible QFT must be renormalizable. If I understand correctly, when this happens, the theory has "asymptotic freedom" and is conformally invariant past some high ...
Davyz2's user avatar
  • 407
4 votes
2 answers
189 views

Role of the natural temperature scale in the anomalous dimension of the renormalization group

In David Tong's lecture notes on statistical field theory, the concept of anomalous dimensions is introduced by considering the scaling of the correlation function $$\langle \phi(\mathbf{x}) \phi(\...
Jasper's user avatar
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16 votes
3 answers
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Why is finding a mathematical basis for the fine-structure constant meaningful?

I was reading QED by Richard Feynman and at the end he mentions that: There is a most profound and beautiful question associated with the observed coupling constant, $e$ – the amplitude for a real ...
Gunnar's user avatar
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1 answer
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Why does integrating out microscopic degrees of freedom lead to the effective free energy rather than the effective energy?

In David Tong's lecture notes on statistical field theory, he considers the partition function of the Ising model and computes the effective free energy by integrating out the microscopic details of ...
VinV's user avatar
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Charge Renormalization in Abelian Gauge Theory under General Gauge Fixing Conditions

In scalar QED or fermionic QED, the relationship between bare quantities (subscript "B") and renormalized quantities is given by $$ \begin{aligned} A^\mu_B &= \sqrt{Z_A} A^\mu\,, \quad \...
ChungLee's user avatar
1 vote
0 answers
55 views

Using the RG equations to find the free energy scaling form of the 2D Ising Model

i am trying to calculate the scaling form of the free energy of the 2D Ising model, starting from it's RG equations: $$\frac{d u_I}{dl} = 2 u_I + u_t^2$$ $$\frac{d u_t}{dl} = u_t$$ $$\frac{d u_h}{dl} =...
Dorek's user avatar
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2 answers
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Why is Perturbative expansion of gravity in terms of $GE^2$?

From General Relativity by Weinberg p.797 edited by Hawking & Israel: This is to be used to generate a perturbation series in powers of $GE^2$ or $G/r^2$ (where $E$ and $r$ are an energy and a ...
Arevilov 3's user avatar
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0 answers
43 views

One-Loop beta function for gauge couplings

I am currently doing my homework on Standard Model one-loop correction. When I am reading Quantum Field Theory by Mark Srednicki and Journeys Beyond the Standard Model by Pierre Ramond, I notice some ...
quantumology's user avatar
32 votes
8 answers
5k views

Explain to a non-physicist what goes wrong when trying to quantize gravity

I am not a physicist, but I'm trying to get a little bit of an understanding of why it is hard to extend the standard model with quantum gravity (i.e. why it's hard to combine QM and GR), cf. e.g. A ...
user56834's user avatar
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0 votes
1 answer
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Loops and UV divergences

I read when asked whether a force could only exist at a certain phase transition or high energy: "I am not aware of a coupling that only exists at high energies or in a phase transition -- in ...
Jtl's user avatar
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1 vote
0 answers
54 views

$Z_1=Z_2$ and its relation to vertex renormalization in QED

I have been working on the full renormalization of scalar QED with self-interactions, following the steps of Schwartz’s treatment on spinor QED (Chap 19). I have 3 main questions regarding this: Need ...
Bcpicao's user avatar
  • 162
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0 answers
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Why the coupling constant in context of different approaches has different energy dependence?

I know that in the language of renormalization group, the coupling constant in the Hamiltonian is dependent of energy, for example in condensed matter physics, of band width. So, we can do a 'poor man'...
Houmin Du's user avatar
1 vote
0 answers
34 views

Evidence of more generations in the QCD beta function

We know that the beta function for QCD is $$ \beta = -\left(11 - \dfrac{2N_f}{3}\right), $$ where $N_f$ is the number of fermions in the theory. We have $\beta_{\text{SM}} = -7$. Now, my question is, ...
Gabriel Ybarra Marcaida's user avatar
3 votes
0 answers
31 views

What are the implications of supersymmetry generators satisfying a majorana condition?

hoping to resolve some confusion I have about this paper (https://arxiv.org/abs/hep-th/9904017) regarding the holographic dual of a flow from ${\cal N}=4$ SYM to an ${\cal N}=1$ SUSY theory. Broadly ...
Cyrus R.O.'s user avatar
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0 answers
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How to study regularity of a Green's function when solving field equations perturbatively?

Preliminaries Consider a nonlinear differential operator $\mathcal{O}$ acting on a field $\phi$, with source $\rho$ $$\mathcal{O}(\phi)=\rho$$ Let's say the charge density is small, so we can define $\...
P. C. Spaniel's user avatar
2 votes
1 answer
397 views

Contribution of dark matter to running of physical constants

I read that "essentially everything in the Standard Model impacts the running of every physical constant in the Standard Model. So, if there is even a single particle missing from the Standard ...
Jtl's user avatar
  • 425
5 votes
1 answer
361 views

Where does Planck's constant come from in non-renormalizability of quantum gravity?

I am trying to understand the idea that gravity breaks down at the Planck scale, but I am confused by the use of natural units ($c = \hbar = 1$). The Einstein-Hilbert action in natural units is: \...
Caspar201's user avatar
2 votes
0 answers
51 views

Renormalization in Background field gauge

The purpose of this question is not very straightforward to explain. So, I just state the question. If we use Background field gauge for renormalization, due to the QED-like Ward identities, the ...
Tanmoy Pati's user avatar
0 votes
0 answers
60 views

Renormalization of the composite operator $\exp(\phi(x))$

I'd like to calculate $\langle\Omega|\exp(\phi(x))|\Omega\rangle$ for quartic scalar field theory (where $|\Omega\rangle$ is the interacting vacuum) and then renormalize to first order in the coupling ...
Jack's user avatar
  • 51
1 vote
0 answers
39 views

Loop Calculations of A Spontaneous Broken gauge theory with fermions

Let me first rephrase the background. Consider adding a massless fermion to the spontaneously broken $U(1)$ gauge theory through a chiral interaction: $$ \mathcal{L}=\bar{\psi}_{L}i \gamma_{\mu}D^{\mu}...
quantumology's user avatar
1 vote
0 answers
36 views

Does the changes of flow regimes of the renormalization group flow diagram imply always that a symmetry has been broken?

Usually we can use RG flow diagrams to understand that a phase transition has happened. Because they are intimately related to a broken symmetry, does that imply that it always implies that a symmetry ...
olsrcra's user avatar
  • 11
2 votes
1 answer
66 views

Why is $F_1(0) = 1$? (form factor in QED)

In section 6.2 in Peskin and Schroeder (P&S) on vertex corrections, it is shown (eq 6.34) that the physical charge of the electron is given by $eF_1(0)$ (as shown by comparing the nonrelativistic ...
User3141's user avatar
  • 863
1 vote
0 answers
58 views

Unitarity and renormalizability in $R_\xi$ and 't Hooft gauge

Consider the massive propagator with gauge fixing $\frac{1}{2a} (\partial A)^2$ $$ \Delta_{\mu\nu}=-i\left[\frac{g_{\mu\nu}}{k^2-m^2}-\frac{k_\mu k_\nu}{m^2}\left(\frac{1}{k^2-m^2}-\frac{1}{k^2-am^2}\...
Tanmoy Pati's user avatar
1 vote
1 answer
55 views

Definition of “quasi-locality” in Wilsonian RG scheme

I’m studying about the holographic RG with this paper. In that paper they say Wilsonian action expects quasi locality, but I’m not sure what “quasi-locality" exactly means. If quasi-locality ...
Positron3873's user avatar
3 votes
0 answers
59 views

Can the Wilson-Fisher fixed point be reached from the massless $\phi^4$ action?

Most textbooks and papers work out the derivation of the Wilson-Fisher fixed point for $\phi^4$ starting from the massive action (in Euclidean space) $$S = \int d^d x \biggl( \frac{1}{2} \partial_\mu \...
Pxx's user avatar
  • 1,723
3 votes
2 answers
64 views

Anomalous dimension must be positive in Ginzburg-Landau $\phi^4$-like theories?

I am trying to understand/find the argument behind a claim made in this paper (page 3, column 1): that the anomalous dimension/exponent $\eta$ of a continuous phase transition in Ginzburg-Landu $\phi^...
bbrink's user avatar
  • 636
2 votes
0 answers
57 views

Distance conjecture being false in $\phi^4$ theory

One part of Distance conjecture states that free theory (Higher spin) are at infinite distance away from any arbitrary point on conformal manifold where the distance is measured with respect to ...
aitfel's user avatar
  • 3,043
5 votes
1 answer
124 views

Why do we rescale momenta after integrating out high momenta in Wilsonian renormalization?

In Section 12.1 of Peskin & Schroeder they motivate Wilson's approach to renormalization by asking how a quantum field theory changes after changing the momentum scale. To answer this they start ...
CBBAM's user avatar
  • 3,350
3 votes
2 answers
128 views

Some integrals in QED Renormalisation

I am currently leaning the renormalisation of QED and I have met some tricky integral that seems unsolvable. The integrals are shown in Quantum Field Theory and the Standard Model by Schwartz, page ...
quantumology's user avatar
2 votes
1 answer
216 views
+50

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 ...
Confuse-ray30's user avatar
3 votes
1 answer
147 views

Schrödinger equation, 2D delta function potential, and confusion

Apropos of nothing in particular, I thought I would play around with the Schrödinger equation in 2D with a delta function potential. To keep things simple I thought I would concentrate on the bound ...
bob.sacamento's user avatar
0 votes
2 answers
122 views

Renormalizability of Quantum Gravity

At the end of chapter 6 on p. 210 in David's Griffiths' book Introduction to Elementary Particle Physics he says that 't Hooft proved that all gauge theories are renormalizable. I have also read ...
KaraboMadisa's user avatar
2 votes
1 answer
146 views

Derivative interactions in the Wilsonian renormalisation Group

I am currently working through some basic renormalisation group problems, and have come to one about derivative interactions. It has been a while since I have studied QFT formally so bear with me ...
Aidan's user avatar
  • 90
3 votes
1 answer
185 views

What is the physical meaning of the counterterms we add in Lagrangians?

I have a probably very silly question. Please help me with it: Say we consider the QCD Lagrangian. All of it's terms involve various fields. Now this Lagrangian can simply be called the Lagrangian of ...
SX849's user avatar
  • 306
1 vote
0 answers
64 views

Reference request scale anomaly

Can anyone recommend some books, notes and review-oriented papers on scale anomaly, with a view towards its relation to renormalization? Such as an anomaly perspective on RG, Callan-Symanzik equations ...
1 vote
0 answers
47 views

What is the interpretation of the $\beta$ and $\gamma$ functions in the renormalization group?

Let $M$ be a renormalization/momentum scale, $\lambda$ a coupling, $G^{(n)}$ the $n$-point Green's function, $Z$ the field strength, and $\Lambda$ a momentum cutoff. When studying the renormalization ...
CBBAM's user avatar
  • 3,350
0 votes
1 answer
113 views

Renormalization group equation, the Callan-Symanzik equation, and renormalization group flow

I am learning about the renormalization group and I am getting confused on some terminology. For the massless $\phi^4$ theory the Callan-Symanzik equation is: $$\big[ M \frac{\partial}{\partial M} + \...
CBBAM's user avatar
  • 3,350
0 votes
1 answer
66 views

Is the magnitude of the $\beta$ function important?

I am currently studying the renormalization group in quantum field theory and have gotten up to computing the $\beta$ function perturbatively . While I only have a basic understanding of it so far, ...
CBBAM's user avatar
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3 votes
1 answer
55 views

Renormalisation in quantum optics

When reading about QED in QFT books, renormalisation seems to be essential to get results eventually. It also seems absolutely necessary even for low energies, since the internal lines lead to ...
lalala's user avatar
  • 1,831
1 vote
1 answer
88 views

Problem solving for Wilsonian Effective Action

I'm currently doing some basic questions on renormalisation group, but I've ran into a wall when it comes to one particular step in an answer. The question is as follows: This problem is a toy model ...
Aidan's user avatar
  • 90
1 vote
1 answer
80 views

Why do correlation functions involving composite fields require special analysis?

For simplicity I will be considering $\phi^4$ theory. To analyze correlation functions of the form $$\langle \phi(x_1)\phi(x_2)\ldots\phi(x_n)$$ with $$x_1 \neq x_2 \neq \cdots \neq x_n \tag{1}$$ we ...
CBBAM's user avatar
  • 3,350
1 vote
0 answers
38 views

How does renormalization affect divergent subdiagrams?

Suppose we have a theory that is super-renormalizable and let $\Gamma^n$ denote the sum of all 1PI diagrams of this theory with $n$ amputated external legs. In such theories, for all $n$ sufficiently ...
CBBAM's user avatar
  • 3,350
4 votes
1 answer
120 views

How do we know at the operator-level that the tadpole $\langle\Omega|\phi(x)|\Omega\rangle=0$ vanishes in scalar $\phi^4$ theory?

I'm a mathematician slowly trying to teach myself quantum field theory. To test my understanding, I'm trying to tell myself the whole story from a Lagrangian to scattering amplitudes for scalar $\phi^...
Nicolas Ford's user avatar

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