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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Fast and slow modes, and the vanishing of certain diagrams during re-normalization

In the middle of pg. 452 of Atland and Simonss Condensed Matter Field Theory, they state the following: Terms of $\mathcal{O}(\phi _{\text{s}}^3\phi _{\text{f}})$ do not arise because the addition ...
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Renormalization condition

Can any on explain to me, why renormalization condition $$\Sigma(\gamma_\mu p^\mu=m)=0,$$ for one loop implies $$\Sigma_2(m)=m\delta_2-\delta_m~?$$ In the original $\Sigma_2$ we had $ m_0$ which is ...
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504 views

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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155 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 \mathbb{...
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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 'l'...
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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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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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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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329 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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Is there a block spin renormalization group scheme that preserves Kramers-Wannier duality?

Block spin renormalization group (RG) (or real space RG) is an approach to studying statistical mechanics models of spins on the lattice. In particular, I am interested in the 2D square lattice model ...
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Wilsonian Renormalisation — Peskin & Schroder Sect. 12.1

I'm working my way through Peskin & Schroeder, but some of the details of the calculations done in their introduction to the renormalisation group are slipping past me. For concreteness, the ...
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Bound states in two and three dimensional delta potential in non relativistic QM

I would like to find bound state energies in let's say 2D delta function potential. So my eigenvalue equation is: $$(-\frac{1}{2}\Delta - g\delta(r)) \psi = -B \psi$$ and by the means of Fourier ...
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What does it mean by “infinities” when dealing with QFT? [closed]

I found this PDF online here while browsing Nobel Prize winner contributions, which explains a bit about renormalization (a concept for which Kenneth G. Wilson won the Nobel). However I was somewhat ...
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Decimation of a triangular lattice [closed]

Consider the network of spins shown below. The Hamiltonian is given by $$H = - \sum_{\langle i j k \rangle} [J \sigma_i \sigma_j \sigma_k + J_0]$$ with $J,J_o \geq 0$ and $\langle i j k \rangle$ ...
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Is a lagrangian with a background field interaction renormalizable ? If yes, when?

Consider the Lagrangian, $$ L = -\partial_{\mu} \chi \partial_{\nu} \chi^{\dagger} - m^2 \chi \chi^{\dagger} + g\chi \chi^{\dagger}\phi,$$ where $\phi$ is a background field and $\chi$ is a complex ...
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49 views

S-matrix element for forward scattering and amputed green function

I'm studying dispersion relations applied as alternative method to perturbation theory from Weinberg's book (Vol.1) Let's consider the forward scattering in the lab frame of a massless boson of any ...
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60 views

multi-dimensional renormalization group flow?

Suppose you have $\lambda \phi^3$ theory, and that you renormalize the 2 and 3 point one-particle irreducible graphs, $\Pi_R(p^2)$ and $\Gamma_R(p_1,p_2,p_3)$, by Taylor expanding about $p=\mu_0$ for ...
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247 views

Beta function calculation in massless minimal subtraction $\phi^4$ theory

I'm trying to understand how to calculate the beta function in massless phi^4 theory using dimensional regularisation and minimal subtraction. I'm struggling to understand: Is it possible to ...
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215 views

One-Loop Yukawa RGEs

I'm currently trying to understand how one can write the one-loop RGEs for the Yukawa couplings using the general formula: One example I'm interested in is how the author derives, using this ...
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Why is the term $m\delta_2\delta_m\bar{\psi}\psi$ ignored in the QED Lagrangian?

Consider the QED Lagrangian $$\mathcal{L}=\bar{\psi}_0(i\gamma^{\mu}\partial_{\mu}-e_0\gamma^{\mu}A_{0\mu}-m_0)\psi_0-\frac{1}{4}(\partial_{\mu}A_{0\nu}-\partial_{\nu}A_{0\mu})^2$$ where the 0 ...
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QFT: What does “finiteness” mean?

As above: what is the definition of a QFT to be "finite"? That all UV corrections are finite and there are no divergences at all? That there are divergences, but these divergences can be absorbed ...
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Rigorous Proof of General Relativity's Non-renormalizability?

The answer to this question and the comments on it implies that general relativity has not been rigorously shown to be non-renormalizable for all loop diagrams -- only shown for two loops. However, ...
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Mass and wave function renormalization In chiral perturbation theory

Before I put forward my actual question, I think it will be useful to set the context in a clear way and that involves my understanding of a few very basic things of Chiral Perturbation Theory. ...
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Statistical field theories on topological defects

Systems like superconductors and superfluids are often treated by specifying some phenomenological mean field theory where the free energy is given as a functional of some order parameter field. Given ...
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Why does regularization work in this Bessel function integral?

I encountered some days before an integral representation for a modified Bessel function and should differentiate it. But in this representation : $$K(\omega,a)=\int_0^{\infty} \frac{ds}{s} e^{-i\...
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Why is it correct to estimate divergences by the cutoff in QFT?

Let's say we have a linear divergence in a quantum field theory. The way to deal with this infinite quantum correction is to go through the whole process of renormalization. However, quite often, ...
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Experimental determination of $\Lambda_{QCD}$

I have a question about $\Lambda_{QCD}$, the energy scale at which there is a transition from the regime of perturbative QCD to quark confinement. How it is measured experimentally?
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Renormalization group and minimum substraction

I have several questions about renormalization group and minimum substraction scheme in particular. My first question is: 1) Why is the beta function typically just a function of coupling? In other ...
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Running of the Higgs mu term (or: running of individual mass terms in a complicated mass matrix)

I am wondering how to calculate the (one-loop) beta function for an individual mass term that appears in combination with a number of other mass terms in the coefficients of a number of fields. What ...
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Books/resources for statistical field theory

I was wondering if anyone knows good, approachable textbook or other resources about statistical field theory (topics like in Kardar's Statistical physics of fields: lattice models, mean field theory, ...
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Physical meaning of RG transformation

When we do RG transformation in Statistical mechanics we eliminate unnecessary degrees of freedom and it leads us to the fixed point. How can I visualize it physically?
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Evaluation of the anomalous dimensions of fields in SUSY $SU(5)$

The general formula for the anomalous dimension can be found in Martin΄s review article (hep-ph/9709356), on page 62 relation (6.5.4). In the case of $SU(5)$ and especially in the paper of Kobayashi, ...
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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: $$ \dfrac{\mathrm{...
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Convergence of light by light scattering amplitude

Perhaps I'm too exhausted to see the answer of why the photon-photon scattering should contain no divergences. In Peskin and Schroeder page 320 we find that because of the Ward identity the photon-...
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Lack of scale in Schrödinger equation for square-inverse potential

I see that if we set our potential in schrodinger equation to be a inverse-square dependence we don't have a typical unit of length as we have for hydrogen atom. $$-{\hbar^2\over 2m}\nabla^2\psi + {\...
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Massless $\phi^3$ theory in $d=6$ dimensions

I am asked to calculate renormalization for a massless $\phi^3$ theory in $d=6$ dimensional space using dimensional regularization. I'm having trouble finding the three-point vertex correction as one ...
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Renormalization of diagrams in QFT [duplicate]

Can any one suggest a good reference for studying renormalization of disjoint, nested and overlapping divergences in Feynman diagrams (for example, $\Phi^4$ theory)?
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One question about renormalization

The idea of renormalization of "naked" perturbation theory is in principal possibility of addition counterterms which reduce infinity when calculating matrix elements. But I have met such concepts as ...
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Anomalies from a Renormaization Group Equation (RGE)

This is an approach to anomalies which seems unfamiliar to me.. Firstly what is this function $W$ which seems to satisfy the equation, $\frac{\partial W }{\partial g^{\mu \nu} } = \langle T_{\mu \...
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O(N) sigma model renormalization

Does anyone know, is a model with lagrangian $\mathcal{L} = \frac{(\partial_{\mu}\phi_a)^2}{2}-\frac{m^2 \phi_a^2}{2}-\frac{\lambda}{8N}(\phi_a \, \phi_a)^2$ renormalizable? I'm using BPHZ scheme and ...
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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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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 Callan-...
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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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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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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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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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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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Does the measure of proximity of two theories in “theory space” run?

From reading this article, I have learned that two effective QFTs can be very close together in the "theory space" appropriate to describe for example physics at the LHC scale, whereas the ...
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Is Bohmian Mechanics incompatible with loop corrections?

For those who continue to be unsatisfied with Quantum Mechanics (QM), Bohmian Mechanics (BM) is an alternative worth considering. It is sometimes claimed that BM is equivalent to QM, but Lubos Motl ...