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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Why do we demand that the counterterms in $\varphi^3$ theory be $O(g^2)$?

In Srednicki's QFT book, section 9, he introduces the $\varphi^3$ lagrangian: $$\mathcal{L}= -\frac{1}{2}Z_\varphi(\partial_\mu\varphi)(\partial^\mu\varphi) -\frac{1}{2}Z_mm^2\varphi^2 +\frac{1}{6}...
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Failing to show $\xi$-gauge-independence in an abelian Spontaneously Broken Gauge Theories (SBGT)

I am studying the following paper: Appelquist, Carazzone, Goldman & Quinn, Renormalization and Gauge Independence in Spontaneously Broken Gauge Theories, https://doi.org/10.1103/PhysRevD.8.1747 ...
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How Does A $\theta$ Angle Shift Affect the Wilsonian Effective Lagrangrian?

Say we have some quantum field theory which includes a gauge field, and some matter, and a topological $\theta$ term so that the Lagrangian reads $$L=(stuff)+\frac{\theta}{64\pi^2}\varepsilon^{\mu\nu\...
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Why doesn't the $\theta$ Angle Renormalize?

The $\theta$ term for Yang-Mills takes the form $$L_{\theta}=\frac{\theta}{64\pi^2}\varepsilon^{\mu\nu\rho\sigma}F^a_{{\mu\nu}}F^a_{\rho\sigma}$$ A fact that I have heard is that $\theta$ does not ...
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Zee's explanation of expressing bare coupling by physical coupling

In terms of bare parameter $\lambda$, the $\phi\phi\to\phi\phi$ scattering amplitude is $\lambda\phi^4$ theory is given by $$\mathcal{M}=-i\lambda+iC\lambda^2\Big[\ln\Big(\frac{\Lambda^2}{s}\Big)+\ln\...
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Terminology: Infrared and Ultraviolet

I am new to high energy physics and string theory. I keep reading the terms infrared and ultraviolet in papers. I assume they aren't talking about electromagnetic radiation. For example, one paper ...
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Question related to electric dipole moment via QFT

My question is related to the following post: Extracting Electric Dipole Moment from Matrix Element via Form Factor There, it is said that the electric dipole moment (EDM) is giving by a term that ...
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rigorous definition of coherence length at mean field theory

so as far as I know, when we are doing mean field theory, in qft, we expand a action of a theory around a classical solution. so we find a classical solution, than we add quantum mechanical ...
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109 views

What goes wrong with GR as a lattice gauge theory?

If one tried to formulate General Realativity in a similar manner to say lattice QCD, what goes wrong that makes it not work? My first thoughts are that for any particular grid, we might have a ...
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Why does the renormalizable theory have only those particles with helicity less than or equal to 1?

Let the helicity operator be $\frac{P \cdot J}{P^0}$ with an eigenvalue $\lambda$. Then why do renormalizable theories have $|\lambda| \le 1?$ (in general dimensions or in 4ds?) Also, what is the ...
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IR divergence Feynman diagram topology query

I am trying to calculate the superficial degree of Infrared divergence. To do this I am reading section 12 of this source. It seems you can calculate it by a method involving the 'shrinking' of ...
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61 views

Counterterms in quantum brownian motion

In the part "Quantum Brownian motion" of the book, The theroy of open quantum systems written by Breuer, the author investigates on the Caldeira-Leggett model: The Hamiltonian of the particle is $H_{...
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Arbitrary function on the Faddev-Kulish dressing

On this paper the authors review the Faddev-Kulish dressing in QED which is a solution to the IR divergence problem. Given one electron momentum $\mathbf{p}$, They define the soft factor by $$F_\ell(...
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80 views

Why does literature list the strong coupling at the scale of the Z-boson's mass?

In the 2004 edition of the book "QCD as a Theory of Hadrons" by S. Narison, the author provides a value for the strong coupling at a scale of the mass of the Z boson, $$ \alpha_s (M_Z) = 0.1181 \pm ...
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Wilsonian RGE: Problem 23.7 in the textbook, M.D. Schwartz's ''QFT and Standard Model'' [closed]

Can anyone give me some hints or directions to work out the solution to the following problem? This problem is from chapter 23 of the textbook written by Professor Schwartz. I can't figure out ...
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Conserved charge during renormalization-group flow

Let us consider a quantum system (at zero temperature) with a continuous (anomaly-free) symmetry $G$ and there exists a corresponding conserved charge $Q$. Then we perturb this (might-be critical) ...
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Quantum expressions for the Virasoro constraints

I am trying to derive the quantum form of the Virasoro constraints. $$ L_{m} = \frac{1}{2} \sum_{n} :\alpha_{m-n}.\alpha_{n}: $$ :...: meaans normal ordering. Using the common commutator between ...
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Divergent integral problem

When expanding the scalar field vacuum energy $$\sum_k \frac{1}{2} \omega_k = \frac{1}{2} (L/2\pi)^{n-1} \int \omega(k) d^{n-1}k = \frac{(L^2/4\pi)^{(n-1)/2}}{\Gamma(\frac{n-1}{2})} \int_0^\infty (k^...
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Euler-Maclaurin formula for path integral

Is there a corresponding Euler-Maclaurin formula for path integral when we divide the path integral into discrete lattice? What is the error correction when we divide the space into lattice of length ...
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Relation between mean field critical point and RG critical point

In the mean field / Landau picture a critical point is where the potential of the order parameter changes curvature. E.g. the mean field potential of a scalar $\phi^4$ theory is $$\mathcal{L} = a t \...
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Nonperturbative results for $\phi^3$ theory in dimensions $d>6$?

The theory is nonrenormalizeable in those dimensions, but can you say anything about the theory anyway? Specifically I am wondering about the status of whether the theory is trivial, i.e. a ...
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Behavior in renormalization group flow that reaches critical point

First question. Does correlation length in renormalization group flow has to be infinite when it eventually reaches critical point? Second question. Why does renormalization group flow keep partition ...
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Can we measure renormalized mass in QFT? [duplicate]

Due to QFT books, we measure pole mass(physical mass) in experiments. From the Lagrangian point of view, renormalized mass is a parameter(in MS bar or some similar renormalization scheme that has an ...
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Renormalization group flow when temperature $T < T_C$, $T_C$ being critical point temperature

Does renormalization group flow have to decrease temperature when $T<T_C$, with $T_C$ being critical point temperature? I think not, but my professor suggests something like that. Maybe I ...
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Why this self-loop diagram is not included in $\phi^4$-theory of Peskin & Schroeder?

Consider a $2\rightarrow2$ scattering process in $\phi^4$-theory. On p. 326 in the book of Peskin & Schroeder, they consider the 3 1-loop corrections in the parenthesis: My question is: Why don't ...
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Taylor expansion in beta function calculation

This post is related to the answer given in Beta function in $\lambda_0\phi^4$ theory The beta function calculus for that theory provides you of $$ \beta(\lambda_p) = - \frac{\epsilon \lambda_p + z\...
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Effective Lagrangians

I get the impression from reading, e.g., this paper, that the term "effective Lagrangian" refers to a Lagrangian derived from a Taylor series expansion of an arbitrary function of known invariants. ...
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Non-renormalizeable Interaction Implies Trivial Interaction?

It has been rigorously proved that the $\phi^4$ theory is trivial, i.e. is a generalized free field, in spacetime dimensions $d>4$. It is also the case that this theory is non-renormalizeable in ...
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Beta function in $\lambda_0\phi^4$ theory

For a real scalar field $\phi$ after performing all the 1-loop renormalization for dimensional regulator $d = 4 - \epsilon,\ \epsilon \rightarrow 0^+$, I have found that the renormalized coupling $\...
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Nonrelativistic Quantum Mechanics Results Implying Analogous QFT Results?

One particularly fascinating example of this I have found is the following. The delta function potential has no effect in nonrelativistic quantum mechanics in spatial dimensions greater than or equal ...
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Triviality of Yang Mills in $d>4$?

It has been proved that the $\phi^4$ theory is trivial in spacetime dimensions $d>4$. By trivial I mean that the field $\phi$ is a generalized free field, or in other words, it's only nonzero ...
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RG of 2D Ising with nonzero magnetic field on triangular lattice

I am given the Ising Hamiltonian \begin{align} H = K \sum_{<ij>}S_i S_j + h \sum_i S_i, \quad K>0 \end{align} to set up a real-space block-spin RG, where the renormalized spins are ...
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Understanding irrelevant operators in Wilsonian RG

I had always understood irrelevant operators as operators whose coefficients got smaller at lower energy scales, but there's a passage from Schwartz's Quantum Field Theory and the Standard Model which ...
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Fractional derivatives in a QFT Lagrangian

There are is at least one question asking about fractional powers of fields in QFT (and why they're not expected to occur), and several others asking about the physical relevance of fractional ...
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Why don't very high order Feynman diagrams contribute significantly?

In a particle physics lecture I had today it was stated that the magnetic moment, $g$, is not quite equal to 2, and the difference is accounted for by QED. Later it was stated that we can see this ...
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Beta function in the Standard Model

In Srednicki's textbook "Quantum Field Theory", Problem 89.4 asks us to compute the leading terms in the beta function for each of the three gauge couplings of the Standard Model. These gauge ...
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How to set the number of fermions in the whole system in fermionic-DMRG program?

In infinite DMRG (density matrix re-normalization group) algorithm, we increase size of super-block by two sites in each iteration. How do we set number of fermions in the system? Let's say we want to ...
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Are there any known models with limit cycles in their RG flow?

The text-book presentation of the renormalization group (RG) leaves one with the impression that all systems will eventually flow to a fixed point. This is somewhat enforced by the phenomenological ...
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How does the generalized effective action in Wetterich's exact RG scheme relate to observables at different scales?

I am not familiar with Wetterich's exact RG paradigm, and cannot understand the main idea behind it. I understand that if one could have solved the model and obtained the all the n-point functions ...
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Does the background shift affects the renormalization group equations?

In Section 21 of "Quantum Field theory" by Mark Srednicki, it is shown that there are two equivalent ways to get the quantum action of the shifted field $\phi'= \phi-\tilde{\phi}$, where $\phi$ is the ...
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Question about DGLAP evolution equation

I am reading chapter 32.2 of Schwartz's QFT book, where he defines the renormalized PDFs $f_i(x, \mu)$. This leads to an equation (32.48), which relates PDFs at different scales $\mu, \mu_1$: $f_i(x,\...
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Is there any connection between instantons and surface-interacting polymers?

Excluded volume polymers interacting with a penetrable hypersurface of variable dimension is a very interesting system to study critical behavior via perturbative renormalization. Since a penetrable ...
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How to deal with fermionic operators in density matrix renormalization group (DMRG)?

Let we have 1D Hubbard model with spinless fermions $$H = -t\sum_i^{L-1} \big(c_i^\dagger c_{i+1}+c_{i+1}^\dagger c_i\big) +V\sum_i^{L-1} n_i n_{i+1}$$ Though this model can be mapped onto XXZ ...
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What's wrong with lattice quantum gravity?

Assume one can write the metric field on a lattice, so on each lattice point one has a value of $g^{\mu\nu}$. Similar to the way lattice QCD is formulated. Then later taking the distance between ...
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Are problems with self-energy of point charge in classical electrodynamics solved by field quantization?

Classical electrodynamics gives strange results when considering a moving charge in its self generated field (Abraham-Lorentz equation). Some 50 years ago there were many efforts and publications ...
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Massless $\phi^4$ theory

Most of the standard textbooks on QFT discuss in some detail the massive $\phi^4$ theory in 4d space-time. I would be interested to see a discussion of massless $\phi^4$ theory (in fact other non-...
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Renormalization of sine gordon theory

So assume that we have a usual sine gordon theory in the the theory we have a term in the hamiltonian $$\frac{yu}{2\pi\alpha^2}\int dx \cos(\sqrt{8}\phi_\sigma(x))$$ where $\alpha$ is cut off ...
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223 views

Superficial degree of divergence in $\lambda\phi^4$

Ryder at the beginning of the chapter about renormalization defines the "superficial degree of divergence" of diagrams in $\lambda \phi^4$ theory. I'll recap the derivation. A diagram in $\lambda\phi^...
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Subtraction scheme invariance in QFT

I'm currently reading Schwartz's QFT text and I'm confused on how observables are supposed to be independent of subtraction schemes. In the text it seems that the renormalized loop diagrams are ...
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Why can we add counterterms?

I'm having a hard time understanding why renormalized perturbation theory works. Why is it permissible to add counterterms to the Lagrangian? Terms which are often divergent themselves and carry ...

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