Questions tagged [renormalization]

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Cluster expansion, Mayer expansion and perturbative renormalization group

This is a second part of my previous question, which I decided to split into two parts not to mix up different topics at one giant question. Again, according to V. Rivasseau (section 1.5 of ...
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What is a large field problem?

I was reading Constructive Renormalization Group by V. Rivasseau and I got some points which I would like to clarify. On page 2, Rivasseau talks about the large field problem and, if I understood it ...
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Cutoff and regularization

Some variant of this question has probably been asked before on this site but my idea is to work with an explicit example. Suppose we discretize the momentum space, so we work with: $$\Lambda^{*} := \...
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1 vote
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Computing kneading sequences for renormalizations of Lorenz maps

I am stuck trying to understand certain claims made in this paper, and for completeness I will reproduce some definitions from it. A Lorenz map $f$ on $I = [0,1]$ is a monotone increasing function ...
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-3 votes
1 answer
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Is the underlying set of every renormalization group countable and finite? [closed]

Is the underlying set of every renormalization group countable and finite? Suppose A is a renormalization group, and the elements of it compose of the set B. Is B the set countable and finite?
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8 votes
1 answer
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From the conceptual idea of the RG to its actual implementation

Everytime I want to understand a little more about the ideas behind Renormalization Group techniques, I get troubled by a gap between the general picture one usually presents (e.g. in books or ...
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Any concrete book for renormalization to recommend?

Any concrete book for renormalization to recommend? concrete Enough,and simple enough, both in mathematics and physics. Thanks in advance.
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3 votes
0 answers
86 views

Regularization of fermionic field theory

My journey into fermionic field theory led me to this very nice paper by M. Salmhofer, which gives an overview of such theories with applications to condensed matter theory. The path integral approach ...
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18 votes
2 answers
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Renormalization in physics vs. dynamical systems

I am studying complex dynamics, so to me renormalization of a dynamical system means something like a rescaled first-return map on (a subset of) the underlying space. I understand that in quantum ...
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6 votes
1 answer
251 views

How can one recover/obtain information from the renormalization group procedure?

I know the basic idea behind the renormalization group approach as it is used in mathematical physics to study both QFT and statistical mechanics. However, I have trouble understanding how can one ...
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8 votes
1 answer
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Non-perturbative Renormalization in the sense of Polchinski's equation. Do we have a mathematical formulation?

My question is about mathematical treatment of exact renormalization group in the sense of Polchinski's flow equation. In a heuristic form, Polchinski's equation looks like: $\partial_t S[\phi] = \...
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1 answer
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Singular Radon probabilities on $[0,1]^d$. Is conditioning on $x_i = \alpha$ well-defined?

The question: Let $\pi$ be a Radon probability measure on $[0,1]^d$, $2\leq d < \omega$, that is singular (w.r.t. to the $d$-dimensional Lebesgue measure). Suppose that for $i\in \{1,\dots,d\}$ and ...
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2 answers
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Formal mathematical definition of renormalization group flow

I was watching some lectures by Huisken where he mentioned that one-loop renormalization group flow was in some analogous to mean curvature flow. I have tried reading up the exact definition of what ...
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4 votes
1 answer
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Why does the type-A subdivision algebra look like the Rota-Baxter algebra axiom?

Let $\mathbf{k}$ be a commutative ring, and $\beta$ an element of $\mathbf{k}$. Fix a positive integer $n$, and set $\left[n\right] = \left\{1,2,\ldots,n\right\}$. The $n$-th type-A subdivision ...
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3 votes
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Renormalization on noncommutative torus

I am reading a paper of renormalization of field theory on noncommutative torus. At the end of chapter 6 there is the following statement "Although our analysis is far from being exhaustive, we ...
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Renorming into contraction

In Pazy's book on semigroups he mentions (page 18) that when you have a commuting family of operators $B(t)$, such that $$ \sup \| B(t_1) .. B(t_n) \| \le M $$ for all finite choices $t_1, .. t_n$ ...
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Renormalization for Transport Equations with SBD velocity field

In the paper Traces and fine properties of a $BD$ class of vector fields and applications by Ambrosio, Crippa and Maniglia (to be found here)the authors prove a chain rule for vector fields $B\in SBD(...
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1 answer
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What are some geometric / physical / probabilistic interpretations of the Riemann zeta function at integer arguments n ≤ 1?

Introduction: This is slightly edited and generalised version of a question I asked on the Physics Stack Exchange website. This question has a twin brother asked here on MO, only now we consider ...
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RG flow and Ricci flow

It looks like the Laplace operator in the nonlinear sigma model (say the Polyakov action) is different from the Laplace-Beltrami operator, how can one get the Ricci flow as a low order approximation ...
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2 votes
1 answer
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Some identities with the Riemann-Hurwitz zeta function

The only definition that I have ever seen of this Riemann-Hurtwitz zeta-function is this, For $0 < a \leq 1$ we have the identity $$ \zeta(z, a) = \frac{2 \Gamma(1 - z)}{(2 \pi)^{1-z}} \left[\sin ...
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1 vote
1 answer
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zeta-function regularized integrals

I gather that the following two identities about $\xi(3)$ hold via some notion of zeta-function regularized integrals. $\xi(3) = \frac{(2\pi)^3}{3}\int _0 ^\infty d\lambda \frac{\sqrt{\lambda} }{1 + ...
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3 votes
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What does the renormalization group flow corresponding to a turbulent subrange with a broad band forcing look like?

In a renormalization group analysis of turbulent flows, such as for example done by Barbi and Münster here who derive an action for the Navier-Stokes equations, insert it into the Wilson equation, and ...
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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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1 answer
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Partial linearization near a hyperbolic fixed point--Classical scattering

I am currently reading the famous article "Universal Properties of Maps on an Interval" by Collet, Eckmann and Lanford related to the Feigenbaum-Coullet-Tresser universality. I am in particular ...
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2 votes
0 answers
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Looking for good summer schools on quantum field theory (especially renormalization theory) this summer [closed]

I'm a graduate student and I'm looking for summer schools to attend this summer. Anyone have any suggestions? Thanks!
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31 votes
5 answers
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What mathematical treatment is there on the renormalization group flow in a space of Lagrangians?

What mathematical treatment is there on the renormalization group flow in a space of Lagrangians?
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13 votes
2 answers
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Simple example of renormalization

As far as I understand, the RG theory, or functional RG theory is a mathematical tool for moving in the "scale dimension". The tool can be used for calculation of Feigenbaums constant (e.g. mentioned ...
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20 votes
2 answers
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Kontsevich's conjectures on the Grothendieck-Teichmüller group?

Reading Kontsevich's "Operads and Motives in Deformation Quantization", I was wondering about the state of the many conjectures concerning the Grothendieck-Teichmüller group in chapter 4. (Also, where ...
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19 votes
2 answers
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Why don't existence and uniqueness for the Boltzmann equation imply the same for Navier-Stokes?

As I understand it, Lions and DiPerna demonstrated existence and uniqueness for the Boltzmann equation. Moreover, this paper claims that Appropriately scaled families of DiPerna–Lions ...
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