Renormalization is an ensemble of techniques which serves to treat the infinities which appear in quantum field theory or statistical mechanics.

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What is the physical meaning of this simplification to calculate the effective coupling constants for a Gaussian model with quartic interactions?

To calculate the effective coupling constants $u'_2(q)$ and $u'_4(q)$ of the effective Hamiltinian eq (4.9) of this paper $$ H' = -\frac{1}{2}\int\limits_q u'_2(q)\sigma'_q\sigma'_{-q} - ...
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226 views

Why is a gaussian fixed point called gaussian?

I know what a gaussian fixed point is, and I did read the wikipedia entry, but it wasn't helpful. It says because the probability distribution is gaussian, but what probability distribution?
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Why is $\rho_m$ proportional to the deviation from critical temperature in critical phenomena?

In Peskin and Schroeder's chapter 12 about the renormalization group, it is stated that the parameter $\rho_m=m^2/M^2$, where $m$ is the mass and $M$ is the renormalization scale, is proportional to ...
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Trace of Fermion Loops in Effective Field Theories

I'd like to know whether we need to take the trace of fermion loops in effective theory in the same way that we need to do so for renormalizable theories. At first thought, it seems obvious that ...
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82 views

Renormalization and the Hierarchy Problem

The hierarchy problem is roughly: A scalar particle such as the Higgs receives quadratically divergent corrections, that have to cancel out delicately with the bare mass to give the observed Higgs ...
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92 views

Quick-and-dirty way to integrate out heavy fields

I understand the roughly understand the process of integrating out heavy degrees of freedom of a Lagrangian, namely, taking the action and performing the path integral over the high momentum modes. ...
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117 views

Misunderstanding Wick Ordering

In M. Salmhofer's "Renormalization, An Introduction" Wick ordering is defined as follows: Let $C = C_\Gamma$ be a nonnegative symmetric operator on $\mathbb{C}^\Gamma$. For $J: \Gamma \to ...
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102 views

Symmetries in Wilsonian RG (2)

This question is related to the paper http://arxiv.org/abs/1204.5221 and is a continuation of the previous question Symmetries in Wilsonian RG In the liked paper why do the equalities in equation ...
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133 views

renormalization group in d=3

Do we really understand why the renormalization group in $d=2+\varepsilon$ and $d=4-\varepsilon$ taking $\varepsilon=1$ gives "good" values for critical exponents in $d=3$? Are they exceptions? Is it ...
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115 views

What's the meaning of the coupling change after a renormalization (in the 1-dim Ising Model)?

What does it mean that after the theory (1-dim Ising model here, but the question is general) is renormalized one time and $g_i\rightarrow g_i'$, that the couplings are weaker, even if the theory ...
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302 views

Identifying a critical phenomena?

I have a system with a number of measurables (in time). Some measurables are discrete some are continuous (within the measurement accuracy). How can I determine whether my system experiences ...
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Observable which dependes on the cutoff

In arXiv:0710.4330v1 Balitsky calculate the eikonal scattering of dipole composed of quark anti-quark, $Tr(U_{x}U^{\dagger}_{y})$, to NLO accuracy. The result he found is: Where $\mu$ is the ...
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107 views

Neglecting mass at asymptotic spacelike momenta

What is the rational/reason for neglecting masses at asymptotic non-exceptional space-like momenta. I have come across this as a first fix for being able to extract information from the ...
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62 views

How to show that tensor gravity is nonrenormalizable?

Let's have the tensor gravity theory, which represented the massless spin-2 field: $$ L = -\frac{1}{32 \pi G}\left( \frac{1}{2}(\partial_{\alpha}h_{\nu \beta}) \partial^{\alpha}\bar {h}^{\nu \beta} - ...
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63 views

Explicit calculation of bosonic string Weyl invariance at one loop

I have been trying to do all the calculations in the Green, Schwarz and Witten Superstring Theory textbook. At the end of chapter 3, the author did one-loop calculation for Weyl invariance for the ...
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94 views

Why do people rule out zeta regularization for renormalization?

Using zeta regularization one can get a formula for regularizing the integral $ \int_{a}^{\infty}x^{m-s}\text dx $ for any $m$. However, I have not seen anywhere. For example, I do not know why in ...
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Relevant operators in two dimensional O(n) models

The most general hamiltonian of a two dimensional $O(n)$ and $Z_2$ invariant statistical model can be written: $$ H=\int d^2 x \left[\frac{\nabla \mathbf{\phi}^2}{2} + \frac{m_0^2}{2}\mathbf{\phi}^2 ...
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What is the relationship between complex time singularities and UV fixed points?

In this paper it is described how the turbulent kinetic energy spectrum and the flatness (a measure for intermittency) are governed by the position of the (dominant) singularities of the solutions of ...
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CP-violation in weak and strong sectors

There is a possible CP-violating term in the strong sector of the standard model proportional to $\theta_\text{QCD}$. In the absence of this term, the strong interactions are CP-invariant. In the ...
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Will Anderson's Poor Man's Scaling loose its effect when band width is small?

The s-d interaction Hamiltonian is as fellows $H_I=Js.S$, J is the coupling strength. We focus on the antiferromagnetic case, where $J>0$. According Anderson's poor man's scaling, the ...
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80 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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98 views

Superstring theory and renormalization [duplicate]

Possible Duplicate: Does the renormalization group apply to string theory? Renormalization in string theory QED and some quantum theories require renormalization techniques and take it as ...
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382 views

What is the meaning of the concepts of “operator mixing” (and anomalous dimensions) [closed]

I am looking for an explanation about the idea of "operator mixing" and its associated concept about when anomalous dimension has to be thought of as a matrix. For example this idea is slightly ...
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150 views

Do perturbative renormalization groups help one understand when perturbation theory can be used in general?

If, as I asked in this question, a relevant operator in a renormalization group transformation can't be used in a perturbative expansion since it becomes large as the transformations are applied, does ...
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312 views

Is the big desert hypothesis a wilder assumption than the see-saw mechanism to explain neutrino masses?

Sometimes I see comments about the big desert hypothesis that I don't understand. For instance in a famous blog : ...This is based on a renormalization group calculation extrapolating the Higgs ...
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140 views

Is the Schwinger action principle important in renormalization?

Is the Schwinger action principle important in renormalization? I want to know if this principle could help us to see if a model is renormalizable of not. If you have any other comment or information ...
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261 views

What is the 'quantum-developed' or 'relativistic-developed' equation of the electrostatic force?

Quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics that is the first theory where full agreement between quantum mechanics, special relativity and ...
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319 views

Can I couple a chiral fermion to electrodynamics?

Or, perhaps, the question is in which circumstances can I couple it, and of these, which are the simplest. For instance, I think that you can not have a massive Dirac fermion and just couple the ...
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155 views

Renormalizibility by power counting

When testing a theory for its renormalizability, in practice one always calculates the mass dimension of the coupling constants $g_i$. If $[g_i]>0$ for any $i$ the theory is not renormalizable. I ...
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220 views

Renormalization: Why is only a finite number of counter-terms allowed?

I have a question please about renormalization in QFT. Why a renormalizable theory requires only a finite number of counter-terms?
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230 views

Quantum gravity and relevant/irrelevant operators

I am familiar with the casual dichotomy in QFT between coupling with positive dimensions in energy implies relevant operator on one side and negative dimension implies irrelevant operator on the other ...
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176 views

Is every QFT non-local in the U.V.?

As much as I understand the renormalization group transformation and the concept of relevant/irrelevant operators, I'd say that if we push the reasoning of only looking at relevant operators when we ...
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158 views

Integrating out high momentum modes in $\phi^4$ theory

I'm trying to follow section 12.1 of Peskin & Schroeder, which describes how integrating out the high momentum modes of the field in $\phi^4$ theory transforms the Lagrangian both by changing the ...
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219 views

Effective operator in four-fermion interaction

In one book, I have got the following lines which I found myself unable to understand what is effective operator? The paragraph is given below: The weak interaction describes nuclear beta decay, ...
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196 views

How to deal with the product of distributions by Renormalization or similar?

how can we deal for example with the product of distributions in physics ?? is there any mean to define with physics $ \delta ^{2}(x) $ or to treat a product of two distributions within the ...
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independence of the bare parameters on μ for beta function

So I know re-normalization has bean "beaten to death". I want to understand something a bit specific which might seem trivial. Independence of the bare parameters on $\mu$ and relevance to the beta ...
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100 views

Amplitudes in renormalized perturbation theory

This question arose while reading Peskin and Schroeder, specifically, it arose in regards to the sum of diagrams above their Eq. (10.20) on pg. 326. The context is $\phi ^4$ theory and they are using ...
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63 views

Nonequilibrium themal QFT

Wick rotation to thermal of QFT in Minkowski space to thermal QFT, which is after this transformation analogue to statistical mechanics, does only describe equilibrium statistical mechanics. On page ...
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88 views

Caimir effect regularization for every divergent sum or series

can we use the tools of renormalization of casimir effect to get finite results for any divergent series in QFT ?? for example let be the divergent series $ \sum_{n=1}^{\infty}n^{l} $ for positive ...
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231 views

Can't find the mass scale; calculation using the modified minimal subtraction scheme and dimensional regularisation

I am taking a course on quantum field theory where there is some confusion regarding the renormalisation scheme we are using (and a corresponding one in my mind). Apparently the lecturer meant MS-bar ...
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135 views

Divergence in Supergravity

I'm not familiar with supergravity so here's my question: I've heard in talks that if one finds divergence for five-loop 4-graviton scattering amplitudes in five dimensions this translates to a ...
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390 views

Why do string theory and Hopf algebra renormalization seem to have no intersection?

Hopf algebra appears in recent papers that systematize renormalization of quantum field theory (QFT). For example see Connes' work and citing papers or a paper referenced here on PSE: R. E. ...
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43 views

Branch cuts in two-point function

The propagator of a QFT is known to have a branch cut as a function of the (complex) external momentum. The branch point (as done by, say, Peskin & Schroeder in eqn.7.19 section 7.1) is ...
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Reference for the renormalization of a scalar field's mass

There are a couple of interesting lectures by Leonard Susskind online, and in the first lecture on Supersymmetry & Grand Unification he explains renormalization. His example is the mass ...
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Peskin's book page 334 proof of $Z_1=Z_2$ to all orders in QED perturbation theory

Peskin in his QFT page 334 argued that $Z_1=Z_2$ to all orders in QED perturbation theory, but I couldn't understand his argument: ... With a generalization of the argument given there (section ...
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Running chargino/neutralino masses in MSSM

Consider the plot below, showing the running of different masses due to renormalization for a certain point of the (c)MSSM. I am able to exactly reproduce the plot, including the running of M1, M2, ...
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171 views

Beta function from exact renormalization group equation

I'm trying to calculate beta functions from exact (or functional) renormalization group equation (I mean Wilson-Polchinski RGE). I've got the equations but I don't know exactly how to use the ...
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How to determine that the renormalization constant $Z_3$ must depend only on $g$ and $\Lambda/m$

In Le Bellac's book, Quantum and Statistical Field Theory, the renormalization constant $Z_3$ is introduced with the equation $$ \Gamma^{(2)}_R(k^2, m^2, g) = Z_3 \Gamma^{(2)}(k^2, m_0^2, g_0; ...
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Running of gauge couplings in the Standard Model [closed]

I'm sure many of us are familiar with the following plot showing the running of the inverse of the fine-structure constants of the SM. (I got the picture from google) At one-loop, the expressions ...
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Field Strength Renormalisation in Peskin and Schroeder

In chapter 7 of Peskin and Schroeder they define the field strength renormalisation $Z$ for a quantum field to be the residue of the Fourier transform of the correlation function $$\langle \Omega | ...