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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How is the apparent significance of (length) scales in physics explained?
From what I understand, especially from reading arguments on Physics.SE, different (length) scales of a system are extremely important. It's clear that if there are two scales $\delta,d,D,\Delta$ with ...
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168 views
Scaling with the Ising Model
I am stuck with one formula in the CFT book by Di Francesco and al. Chapter 3. Equation 3.46 third step, for those who don't have the book, he integrates out degrees of freedom from the Ising Model by ...
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173 views
How to perform a scale (invariance) transformation?
According to this wikipedia article in the $\phi^4$ section, the equation
$$\frac{1}{c^2}\frac{∂^2}{∂t^2}\phi(x,t)-\sum_i\frac{∂^2}{∂x_i^2}\phi(x,t)+g\ \phi(x,t)^3=0,$$
in 4 dimensions is invariant ...
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Significance of massive states in string theory
A free superstring has an infinite tower of states with increasing mass. The massless states correspond to the fields of the corresponding SUGRA. In "Quantum Fields and Strings: A Course for ...
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Do perturbative renormalization groups help one understand when perturbation theory can be used in general?
If, as I asked in this question, a relevant operator in a renormalization group transformation can't be used in a perturbative expansion since it becomes large as the transformations are applied, does ...
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Question about the perturbative renormalization group
I'm currently learning about the renormalization group (RG) in condensed matter physics and just want to clarify a couple of things:
When doing the RG transformation, there's a flow to a fixed point. ...
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1answer
177 views
Why is a gaussian fixed point called gaussian?
I know what a gaussian fixed point is, and I did read the wikipedia entry, but it wasn't helpful. It says because the probability distribution is gaussian, but what probability distribution?
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Values of SM parameters at one certain scale
The general question is:
What are the values of Standard Model parameters (in the $\bar{MS}$ renormalization scheme) at some scale e.g. $m_{Z}$? As its parametrization in Yukawa matrices is not unique ...
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How can one build a multi-scale physics model of fluid flow phenomena?
I am working on a problem in Computational Fluid Dynamics, modeling multi-phase fluid flow through porous media. Though there are continuum equations to describe macroscopic flow (darcy's law, ...
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253 views
Is there a Non-perturbative renormalization algorithm? [duplicate]
Possible Duplicate:
is there non-perturbative RENORMALIZATION ?? if so how it works?
Is there a non-perturbative renormalization algorithm ???, for example to avoid the divergent integrals ...
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How to prove equivalence of RG flow of QFT coupling constant and diagrammatic resummation at fixed renormalization scale?
QFT books say that solving the RG equation $\frac {dg} {d\textbf{ln} \mu}=\beta(g)$, using the one-loop beta function, is to the "leading log" approximation equivalent to resumming infinitely many ...
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630 views
Simple (but wrong) argument for the generality of positive beta-functions
In the introduction (page 5) of Supersymmetry and String Theory: Beyond the Standard Model by Michael Dine (Amazon, Google), he says
(Traditionally it was known that)
the interactions of ...
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conformal anomaly of free scalar in 2D
I'm trying to calculate the conformal anomaly $c$ of a free scalar on a 2-sphere. I've seen other, indirect ways to do this, but since this is a free theory I feel like it should be possible to see ...
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2answers
246 views
Have experiments ever suggested two different values to the same divergent series?
I believe to have understood that some physical experiments suggest finite values to divergent series (please correct me if I'm wrong, my understanding of these matters is limited).
I heard, for ...
10
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4answers
727 views
QM and Renormalization (layman)
I was reading Michio Kaku's Beyond Einstein. In it, I think, he explains that when physicsts treat a particle as a geometric point they end up with infinity when calculating the strength of the ...
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143 views
Regularization of the Casimir effect
For starters, let me say that although the Casimir effect is standard textbook stuff, the only QFT textbook I have in reach is Weinberg and he doesn't discuss it. So the only source I currently have ...
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Nuclear physics from perturbative QFT
Is there a renormalizable QFT that can produce a reasonably accurate description of nuclear physics in perturbation theory? Obviously the Standard Model cannot since QCD is strongly coupled at nuclear ...
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Is renormalization associated with a volume scale or with an energy-momentum and length scale?
Given that real-space renormalization blocks together small volume elements to construct larger volume elements, is it more appropriate/helpful to consider the renormalization scale to be a volume ...
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2answers
394 views
Zeta-function regularization in QFT for heat kernels
When one is doing zeta-function regularization of the heat-kernel for QFT then one is doing these following steps,
the integral over the imaginary time
taking the trace of the heat-kernel or the ...
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1answer
75 views
Derivatives of fluctuations about a condensate
Firstly I am not sure as to whether I am using the word "condensate" in the right context. In QFT contexts I think I see it getting used to mean the space-time independent solution which would solve ...
10
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1answer
796 views
How to interpret vacuum instability of Higgs potential
If the Higgs mass is in a certain range, the quartic self-coupling of the Higgs field becomes negative after renormalization group flow to a high energy scale, signalling an instability of the vacuum ...
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Why regularization?
In quantum field theory when dealing with divergent integrals, particularly in calculating corrections to scattering amplitudes, what is often done to render the integrals convergent is to add a ...
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Renormalization Group for anisotropic “Gaussian” model
I'm considering an "anisotropic" Hamiltonian of the form
$$\beta H = \int d^n r_{||} d^{d-n} r_{\bot} \frac{K}{2} (\nabla_{||} m)^2 + \frac{L}{2} (\nabla^2_\bot m)^2 + \frac{t}{2}m^2 - hm$$
which in ...
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Renormalization Group: Different fixed points
Extending the Gaussian model by introducing a second field and coupling it to the other field, I consider the Hamiltonian
$$\beta H = \frac{1}{(2\pi)^d} \int_0^\Lambda d^d q \frac{t + Kq^2}{2} ...
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2answers
143 views
RG of the Gaussian Model: Finding the scaling factor
I'm studying how the Renormalization Group treatment of the simple Gaussian model,
$$\beta H = \int d^d r \left[ \frac{t}{2} m^2(r) + \frac{K}{2}|\nabla m|^2 - hm(r)\right]$$
In momentum space, the ...
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Geometric entropy vs entanglement entropy (dependent on curvature coupling parameter)
I have a quick question. In hep-th/9506066, Larsen and Wilczek calculated the geometric entropy (which I believe is just another name for entanglement entropy) for a non-minimally coupled scalar field ...
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1answer
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Derivation of Eq. 7.12 in the review paper of Kraus
I'm reading "Lectures on black holes and the $AdS_3/CFT_2$ correspondence" by Kraus.
http://arxiv.org/abs/hep-th/0609074
I don't know how one can obtain Eq.7.12. My stupid question is how to obtain ...
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1answer
407 views
Explanation of Cardy's “a theorem”
There seems to have been some discussion of Cardy's "a-theorem" recently:
“It is shown that, for d even, the one-point function of the trace of the stress tensor on the sphere, Sd, when suitably ...
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2answers
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Possible research implications of proof of John Cardy's a-theorem in QFT
According to this recent article in Nature magazine, John Cardy's a-theorem may have found a proof.
Question:
What would the possible implications be in relation to further research in QFT?
...
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7answers
375 views
Is 'now' smeared over time?
Conventional physics as is usually presented in textbooks deals with the evolution of states in phase space parameterized by sharp instances in time, a real parameter. However, quantum fluctuations ...
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2answers
54 views
Infinity of running couplings
A Landau pole - an infinity occurring in the running of coupling constants in QFT is a known phenomena. How does the Landau pole energy scale behave if we increase the order of our calculation, (more ...
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Renormalization scheme independence of beta function
I have some questions about renormalization. To my understanding, in order to deal with infinities that appear in loop integrals, one introduces some kind of regulator (eg, high momentum cutoff, ...
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Supersymmetric Nonrenormalization Theorems
I'm looking for approaches to nonrenormalization theorems in supersymmetric QFT which are as much as possible mathematical, elegant and involve few heavy straightforward computations
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1answer
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What is the significance of the branch cut in renormalization group logarithms?
What is the physical significance of the branch cut in renormalization group logarithms?
(Is this just an avatar of the optical theorem, or is there something to be understood about these logarithms ...
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2answers
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Renormalization in string theory
I'm taking a course in string theory and have encountered renormalization for the first time (and I suspect it isn't the last).
Specifically, while quantizing the bosonic and spinning strings, an ...
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1answer
102 views
Holographic Renormalization in non-AdS/non-CFT
In AdS/CFT, the story of renormalization has an elegant gravity dual. Regularizing the theory is done by putting a cutoff near the conformal boundary of AdS space, and renormalization is done by ...
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Can I couple a chiral fermion to electrodynamics?
Or, perhaps, the question is in which circumstances can I couple it, and of these, which are the simplest.
For instance, I think that you can not have a massive Dirac fermion and just couple the ...
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4answers
564 views
Is QFT mathematically self-consistent?
After recently going through a short program of self-study in quantum mechanics, I was surprised to find a quote attributed to Feynman essentially saying he was extremely bothered by the computational ...
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1answer
208 views
Renormalizing Chaos: Transition in a Logistic Map
I am currently trying to understand the analysis of a logistic-like map $$f_\mu (x) = 1-\mu x^2$$
after section 2.2 in "Renormalization Methods" by A. Lesne.
As I understand it, the physical ...
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2answers
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Renormalization Group for non-equilibrium
For equilibrium/ground state systems, a (Wilson) renormalization group transformation
produces a series of systems (flow of Hamiltonians/couplings $H_{\Lambda}$ where $\Lambda$ is the cut-off) such ...
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3answers
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Continuum theory from lattice theory
I am looking for references on how to obtain continuum theories from lattice theories. There are basically a few questions that I am interested in, but any references are welcome. For example, you can ...
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2answers
291 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 ...
6
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1answer
330 views
Why Zeta regularization is not valid for multiple-loops?
Why zeta regularization only valid at one-loop?
I mean there are zeta regularizations for multiple zeta sums.
Also we could use the zeta regularization iteratively on each variable
to obtain finite ...
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Are there books on Regularization and Renormalization in QFT at an Introductory level?
Are there books on Regularization and Renormalization, in the context of quantum field theory at an Introductory level? Could you suggest one?
Added: I posted at math.SE the question Reference ...
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Superfields and the Inconsistency of regularization by dimensional reduction
Question:
How can you show the inconsistency of regularization by dimensional reduction in the $\mathcal{N}=1$ superfield approach (without reducing to components)?
Background and some references:
...
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1answer
378 views
Does the renormalization group apply to string theory?
Can we implement a scale dependent cutoff Λ to string theory? Can we perform a renormalization group analysis of string theory consistently?
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Does renormalization make quantum fields into (slightly) nonlinear functionals of test functions?
Quantum fields are presented as operator-valued distributions, so that the operators in the theory are linear functionals of some test function space. This works well for free fields, giving us a ...
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Who works professionally on reformulation of QFT?
P. Dirac was worried with the infinities and their discarding in QED. He wanted us to reformulate the theory in order to eliminate infinities and renormalizations from the very beginning. Is there ...
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The Reeh-Schlieder theorem and quantum geometry
There have been some very nice discussions recently centered around the question of whether gravity and the geometry and topology of the classical world we see about us, could be phenomena which ...
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1answer
250 views
running of coupling constant as a function of distance?
There are many papers about the running of coupling strength as a function of momentum/energy scale,
but are there any experimental papers about coupling strength as function of distance?
Also, are ...
