Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [renormalization]

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

1
vote
1answer
29 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_{...
1
vote
0answers
24 views

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(...
1
vote
1answer
46 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 ...
1
vote
0answers
31 views

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 ...
1
vote
0answers
19 views

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) ...
1
vote
0answers
30 views

Integral calculation: finding the correct ansatz

I have already asket this question, but I would like to reask it and add some details. Let us consider the following integral $$I^{\mu\nu}=\int_{0}^{\pi}d\theta\,\sin\theta\frac{f^{\mu}f^{\nu}}{1-\cos\...
2
votes
1answer
48 views

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 ...
0
votes
1answer
41 views

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^...
2
votes
0answers
67 views

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 ...
2
votes
0answers
16 views

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 \...
1
vote
0answers
40 views

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 ...
1
vote
1answer
59 views

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 ...
0
votes
0answers
34 views

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 ...
1
vote
1answer
31 views

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 ...
0
votes
0answers
49 views

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\...
1
vote
1answer
53 views

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. ...
2
votes
1answer
63 views

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 ...
1
vote
1answer
97 views

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 $\...
4
votes
1answer
74 views

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 ...
3
votes
2answers
124 views

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 ...
2
votes
0answers
45 views

Luttinger model, conform field theory and RG

I'm studying the Luttinger model and I'm having a hard time understanding its relation with conformal field theory. I'd like to know something about this. Is the Luttinger model conformal only at ...
1
vote
0answers
32 views

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 ...
5
votes
1answer
71 views

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 ...
1
vote
1answer
37 views

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 ...
15
votes
3answers
263 views

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 ...
2
votes
1answer
95 views

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 ...
0
votes
0answers
29 views

Two methods to find critical exponents from renormalization-group equations

Consider a renormalization-group flow for a set of quantities $(x_1, ..., x_N) \equiv \bf x$, which can be written in the form ${\bf x}_{t+1} = {\bf F}[{\bf x}_t, T]$,where $T$ is the temperature. At ...
2
votes
0answers
19 views

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 ...
8
votes
2answers
109 views

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 ...
1
vote
0answers
34 views

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 ...
4
votes
0answers
42 views

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 ...
0
votes
0answers
109 views

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,\...
1
vote
0answers
14 views

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 ...
1
vote
0answers
70 views

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 ...
0
votes
0answers
71 views

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 ...
2
votes
1answer
52 views

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 ...
1
vote
0answers
53 views

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-...
3
votes
1answer
83 views

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 ...
0
votes
1answer
75 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^...
2
votes
1answer
58 views

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 ...
5
votes
4answers
183 views

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 ...
2
votes
1answer
28 views

Running coupling constants within a highly compressed object

I wonder is it possible. in highly compressed objects, such as neutron stars and black holes, (I'm not sure that this applies to singularities), that the physical conditions within these objects ...
2
votes
1answer
75 views

Why does the Lagrangian Density have to be a polynomial of the field?

In a lecture, a professor appeared to have said that the Lagrangian can only contain terms that have powers of $\phi$ and a term with $\partial_\mu \partial^\mu \phi$ . I imagine this would make any ...
0
votes
0answers
41 views

Finding ground state energy using numerical real space renormalization group

I want to find ground state energy (as well as wavefunction) for spinless $tV$ model using Real-Space Renormalization Group (RSRG) approximation. The $tV$ model is defined as $$H=H_t+H_{int}=-t\sum_{i=...
5
votes
1answer
105 views

Is there any relation between density matrix renormalization group (DMRG) and renormalization group (RG)?

Probably I am going to receive many down-votes for this post but I really need to ask this question here. I am new to statistical mechanics. I wanted to learn Density Matrix Renormalization Group (...
2
votes
1answer
88 views

${\cal N} = 1$ SUSY Non-renormalization theorem

In Ref. 1, on Page 53, the ${\cal N} = 1$ SUSY non-renormalization theorem is derived. One first specifies the symmetries of the general ${\cal N} = 1$ SUSY action in the superspace formalism, and ...
3
votes
0answers
33 views

What would a non-perturbative renormalization group treatment for polymers look like?

I know that one can do perturbative renormalization for the polymer excluded volume problem or the self-avoiding walk problem corresponding to n=0 component field theory. Here in Hamiltonian, we have, ...
2
votes
3answers
212 views

What is the publication through which Zinn-Justin published what has come to be known as the “Zinn-Justin equation”?

does anybody know which publication contains the introduction of what has come to known as the Zinn-Justin equation?
4
votes
1answer
109 views

For dimensional regularization, why the arbitrary mass scale $\mu$ has the meaning of UV cutoff?

For sharp cut off regularization, we introduce the UV cutoff $\Lambda$. When we need to do momentum integral, we integrate the momentum ball with radius of $\Lambda$. This $\Lambda$ has the explicit ...
2
votes
0answers
70 views

Why is the standard model renormalizable if we believe it is an effective theory? [duplicate]

We believe that the standard model is only an effective field theory of its true UV completion. However, effective theories have dimensionful couplings and are not renormalizable. The standard model ...