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Questions tagged [renormalization]

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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(Coleman's lecture note) scattering in QFT

I am currently reading Coleman's lecture note on QFT.(https://arxiv.org/abs/1110.5013) I have several questions regarding the scattering theory. Let $\phi$ be a real scalar field, and consider the ...
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What's the exact relationship between the scale $Q$ at which parameters are probed and the “fake parameter” $\mu$?

It is well known that couplings change depending on the scale $Q$ at they are measured. This effect is experimentally well documented: From a theoretical point of view, the running $\alpha_S(\mu)$ ...
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Kosterlitz-Thouless transition and renormalisation group theory [closed]

I'm trying to understand the Kosterlitz-Thouless transition in 2d systems. There is a section in Altland and Simons' Condensed Matter Field Theory that discusses the phenomenon, but I don't really ...
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What's the difference be Wilsonian and continuum EFT?

In his review on Effective Field Theory, Georgi emphasizes Within the general framework of the effective field theory idea, there are two rather different approaches, which I will call the Wilson ...
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Regularization is mandatory. What about renormalization?

We need to regularize in order to declare with confidence that infinities drop out from measurable quantities, e.g. in the form of a cutoff scale. In general, the amplitudes in QFT depend on the ...
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How do we end up with the renormalization group equations in the Wilsonian perspective?

We start with a Lagrangian $L$, which is valid up to some scale $\Lambda$ and includes couplings $g,m$. In the Wilsonian perspective, we note that the contributions from fluctuations at scales ...
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Why sharp cutoff RG introduces long range interaction and smooth cutoff doesn't

In momentum shell RG we introduce a sharp momentum cutoff, and integrate out those high momentum modes to get an effective action. I heard that this kind of RG will introduce long range interaction, ...
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Why the randomness in glass/water/air does not destroy coherence of light over fairly macroscopic scales?

When light passes through glass/water/air, photons are absorbed and re-emitted by the chemical bonds, so that the speed of light in medium is reduced. However, in these media, it would appear that the ...
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Why can a renormalizable quantum field theory only include spin 0, 1/2 and 1 fields?

Hitoshi Murayama writes in his 221A Lecture Notes on Spin How do we choose spin when you introduce a field, then? A consistent ( i.e. , renormalizable) quantum field theory can include only spin 0, ...
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Where the derivative corrections come from in Wilson renormalization?

I known that in the Wilson renormalization process fast modes are integrated out in order to define an effective action for the low modes field. Considering phi to the fourth theory it's easy to see ...
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Why is quantum gravity non-renormalizable?

The book The Ideas Of Particle Physics contains a brief treatment of quantum gravity, in which the claim is asserted that if one attempts to construct a model of gravity along the same lines as QED, ...
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Wheeler-deWitt equation as a renormalization group flow

I recently heard a comment that Wheeler-deWitt equation can be interpreted as RG flow equations. However, I haven't been able to find appropriate references for the same. Could someone suggest any ...
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One-loop corrections to vacuum polarization with a specific Lagrangian

I'm having some difficulties regarding this problem in QFT I'm doing to prepare for an exam. For the following problem I consider the theory described by the Lagrangian: $$\mathcal{L}=-\frac{1}{4}F_{\...
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Why don't we add Wilson loops to the SM Lagrangian?

As the title says: why don't we add Wilson loops to common Lagrangians such as the Standard Model? They're gauge invariant and (correct me if I'm wrong, not sure on that) are renormalizable. Suppose ...
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Why/When would one study Renormalization Group flow of a system?

It is not that I am looking for a cheap way out of reading a book about RG flow, but I would like to know few key insights that RG flow study provides, backed with some specific examples. I know a ...
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What are the necessary or sufficient conditions for a renormalization group scheme to be “valid”?

Suppose I have a super operator $G$ which acts on Hamiltonians to produce a new Hamiltonian that is related somehow. For the purposes of this question, suppose that these Hamiltonians are defined on ...
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Tadpole diagrams in 1-loop massive scalar amplitudes?

Consider a massive scalar diagram such as or The loop momentum enters and exits the tadpole vertex, so that in the first diagram the momentum in the propagator connecting the two vertices is zero ...
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Is it possible to define a real space renormalization group scheme for a lattice where the local Hilbert space dimension increases?

I'm currently looking at a way of renormalizing a particular Hamiltonian. One of the questions I'm currently trying to answer is whether, in a renormaliztion group (RG) flow, it is valid to allow the ...
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Peskin and Schroeder Section 7.1 Mass Shift

I'm slowly reading my way through Peskin and Schroeder. Near the end of section 7.1 they compare the mass shift of the electron from QFT to the classical value, both of which are divergent but in ...
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Bare mass versus the mass form spontaneous symmetry breaking

Consider renormalization in $\phi^4$ theory $$\mathscr{L}=(\partial\phi)^2-\frac{1}{2}m^2\phi^2+\frac{\lambda}{4}\phi^4$$ where $m$ and $\lambda$ are respectively the unobservable bare mass and bare ...
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In relativistic QFT, is it ever possible that the bare mass be finite and equal to the physical mass?

In renormalization, one follows the philosophy that the bare mass is unobservable and could be infinite, and the physical mass comes from the pole of the two-point function. Is it possible that in any ...
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72 views

Renormalization constants

I would like to understand how to extract renormalization constants of vacuum polarization diagram in pseudoscalar Yukawa theory with interaction $ig\bar{\psi}\gamma^5\psi$. This diagram is ...
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Is the Standard Model UV complete? If not, why? [duplicate]

Below is my understanding of why QED is not UV complete. Please correct me if I am wrong. As a necessary condition, a UV complete quantum field theory must be renormalizable. But a renormalizable ...
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Existence of interacting scalar field theory

I saw a comment in Schwartz's introductory text on Quantum Field Theory (cf. Section 14.5) that it is known that $\phi^4$ theory in five dimensions does not exist. In four dimensions it is not known, ...
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Reference for proof of renormalizability

I have been trying to truly understand the renormalizability of quantum (i.e., without anomalies) gauge theories (after which I will focus on the case with spontaneous symmetry breaking). The problem ...
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Feynman diagrams, Feynman rules and corresponding integrals

I would like some basic examples of Feynman diagrams: in particular I would like to understand how a Feynman diagram produces an integral: before I start let me made some remarks in the form of a ...
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If a RG fixed point (FP) is CFT, do all theories flowing into FP CFTs?

Suppose that a RG (renormalization group) fixed point of some RG trajectory (or flow) is a CFT. Then do theories in this trajectory have to be CFTs as well?
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What does Pauli-Villars Regularization physically mean?

Calculating loop correlators, Pauli-Villars regularization is introduced to avoid divergence. It is to cut off the high frequency(loop-momentum) contribution. Thus a question naturally arises. Why is ...
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Renormalization Group - Scaling fields and physical critical exponents (1D Ising model)

This is related to this question: Critical exponents and scaling dimensions from RG theory. TLDR: How to compute physical critical exponents $\alpha, \beta, \gamma, etc$ from the RG exponents when ...
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$\beta$ function for the Gross-Neveu model

In the Peskin & Schroeder textbook, the $\beta$-function for the Gross-Neveu model is discussed in problem 12.2. After computing it, I have tried checking my results with some solutions found ...
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Integrability condition of perturbations of Wess-Zumino-Witten (WZW) models

When one tries to analyze the renormalization group of marginal perturbations of Wess-Zumino-Witten (WZW) model in 1+1d, only those "integrable perturbations" can be computed analytically. I wonder ...
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Instantons, renormalization, and the Schwinger Model

Instantons in QCD contribute to the up, down, and strange quark masses (see, e.g., Georgi and McArthur (1981) or Kaplan and Manohar (1986)). Some papers claim that this contribution is equivalent to ...
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Why is the relation $M_W=M_Z\cos\theta_W$ true only at tree-level?

In Glashow-Weinberg-Salam electroweak theory, the relation $$M_W=M_Z\cos\theta_W\tag{1}$$ is said to be remain true only at the tree-level; it receives corrections from the loop diagrams. See here. ...
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Renormalization of the Wess Zumino Witten term

I was learning about the Wess-Zumino-Witten model and I encountered the the following 2-dimensional Lagrangian $$ \mathcal{L} = \frac{1}{4\lambda^2} \text{Tr}(\partial_\mu g ~\partial^{\mu} g^{-1}) + ...
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What is the way to work out the running of lepton masses?

If we assume the GUT unification energy is some value E, (say $10^{16}GeV$). Can we work out the running of the particle masses for example the electon, muon and tau at various energies? And will ...
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Wavefunction Renormalization in Wess-Zumino Model

In Modern Supersymmetry: Dynamics and Duality, on page 134 and 135 in section 8.2, the authors studied the wavefunction renormalization of the Wess-Zumino model. The kinetic terms are given by $$\...
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Would Color Confinement apply in higher dimensions?

As I understand it color confinement comes from the fact that as the distance between two color charges increases the color potential energy increases, instead of decreasing, and the energy needed to ...
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135 views

Why coupling constants with negative mass dimensions lead to non-renormalizable theories?

can somebody explain or point to the relating mathematics showing Why coupling constants with negative mass dimensions lead to non-renormalizable theories?
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Scaling limit of the Ising model with nonzero order parameter

I'm interested in simulating the continuum limit of the 2D Ising model $$H=J\sum_{\langle i j\rangle} s_i s_j+ h \sum_i s_i$$ In one dimension I can fix average magnetization $m=\langle s\rangle$ and ...
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How scale invariance is broken in nature?

By definition a system will exhibit scale invariance at low energies if it has an IR fixed point. I am having some doubts on how to interpret this fact in terms of quantum field theory and to ...
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Dimensional regularisation in $\phi^4$ theory

My question is in regards to the 1-loop corrections of phi 4 theory. The question is in regards to these notes: http://www.damtp.cam.ac.uk/user/dbs26/AQFT/chap5.pdf On page 15 of these notes (PDF ...
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Scaling dimension and system size

I am reading a paper (Sliding Luttinger liquid phases ) which is trying to obtain the scaling dimension of several operators in (condensed matter) field theory. In this paper, the authors mentioned ...
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What Lagrangian counterterms might be needed in a $\phi^ 6$ theory in 3D?

Assuming a massive $\phi^6$ theory in $d=3$ given by the Lagrangian $$\mathcal L=\frac{1}{2}(\partial\phi)^2-\frac{1}{2}m^2\phi^2-\frac{\lambda}{6!}\phi^6 +\mathcal L_\text{ct},$$ what are the counter ...
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A question about renormalization condition and Callan-Symanzik equation

In Ch.12 of the textbook An Introduction to Quantum Field Theory by Peskin and Schroeder, on P.408 the renormalization conditions are given at the energy scale $M$ $$\mathrm{dressed\ 4\ point\ vertex}...
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What happens to renormalisation counter-terms in the classical limit?

My understanding is we add counter-terms to the actions in the process of renormalisation. Presumably these terms don't have a physical effect in a classical interpretation of the action. i.e. they ...
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A Question about In/Out States in Quantum Field Theory

When I was reading the lecture notes Advanced Quantum Field Theory by Jorge Crispim Romao, I accidentally found the following thing that I don't understand. On page 56, section 2.2, the author ...
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Is the term “quantum triviality” defined by the UV or the IR behavior of the RG flow?

The Wikipedia page on quantum triviality seems to give two different definitions for the term that are not obviously equivalent. Some parts of the page seem to define a renormalizable theory as "...
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120 views

Partition function in renormalization

When studying statistical mechanics, renormalization is understood from attempts to calculate partition function by simplifying. (For example, David Tong's lecture note) While I understand that ...
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Asymptotically free/flat

What does the expression: "...the theory becomes asymptotically free/conformal" mean? If it means that the spacetime $M$ on which the fields are defined is e invariant under conformal ...
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126 views

Renormalisation group flow of the $\phi^4$ theory

I am reading Peskin & Schroeder about the renormalisation group flow of the $\phi^4$ theory: $${\cal L} = \frac{1}{2}(\partial_\mu\phi)^2 +\frac{1}{2}m^2\phi^2 + \frac{\lambda}{4!}\phi^4 $$ P &...