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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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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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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Suggested reading for renormalization (not only in QFT)
What papers/books/reviews can you suggest to learn what renormalization "really" is? Standard QFT textbooks are usually computation-heavy and provide little physical insight in this respect - after my ...
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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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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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A pedestrian explanation of Renormalization Groups - from QED to classical field theories
shortly after the invention of quantum electrodynamics, one discovered that the theory had some very bad properties. It took twenty years to discover that certain infinities could be overcome by a ...
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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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Why should the Standard Model be renormalizable?
Effective theories like Little Higgs models or Nambu-Jona-Lasinio model are non-renormalizable and there is no problem with it, since an effective theory does not need to be renormalizable. These ...
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Why is gravity so hard to unify with the other 3 fundamental forces?
Electricity and magnetism was unified in the 19th century, and unification of electromagnetism with the weak force followed suit, bringing into play the electroweak force.
I've been told that ...
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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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Multi-loop beta function of gauge theory (*without* Feynman diagrams)
I would like to point to the beautiful section 4.3 (page 42) of these lecture notes. I think this is the most educative exposition I have ever seen anywhere about Yang-Mill's beta function. What I ...
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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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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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What is a good mathematical description of the Non-renormalizability of gravity?
By now everybody knows that gravity is non-renormalizable, what is often lacking is a simplified mathematical description of what that means. Can anybody provide such a description?
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What is the relation between renormalization in physics and divergent series in mathematics?
The theory of Divergent Series was developed by Hardy and other mathematicians in the first half of the past century, giving rigorous methods of summation to get unique and consistent results from ...
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1answer
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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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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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7answers
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What are the uses of Hopf algebras in physics?
Hopf algebra is nice object full of structure (a bialgebra with an antipode). To get some idea what it looks like, group itself is a Hopf algebra, considered over a field with one element ;) usual ...
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4answers
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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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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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1answer
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Why do irrelevant operators require infinitely many counterterms?
As far as I understand it, in the Wilsonian picture of renormalization, we view a theory as having some fixed cutoff and bare couplings, and integrate out high-momentum modes to understand what ...
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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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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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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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Symmetries in Wilsonian RG
I wanted to know if there is a theorem that in writing a Lagrangian if one missed out a term which preserves the (Lie?) symmetry of the other terms and is also marginal then that will necessarily be ...
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2answers
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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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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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Radial quantization and infrared divergences
I am reading Ginspard lectures "Applied CFT" http://arxiv.org/abs/hep-th/9108028 which is not my first material on the subject. He tries to motivates radial quantization on the reason that ...
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Can modern twistor methods to calculate scattering amplitudes be applied to renormalization group calculations?
As explained for example in this article by Prof. Strassler, modern twistor methods to calculate scattering amplitudes have already been proven immensely helpful to calculate the standard model ...
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2answers
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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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1answer
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What is the Principle of Maximum Conformality?
I'm trying to understand this article about an advance in the theoretical understanding of QCD which centers on the Principal of Maximum Conformality. What is this Principle? In other words, what is ...
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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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1answer
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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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How can perturbativity survive renormalization?
The most usual way to renormalize quantum field theories is by re-writing the Lagrangian in terms of physical (finite) parameters plus counter-terms. Take $\lambda \phi^4$ theory for instance:
$$
...
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Could motives aid in the study of the Navier-Stokes equations?
Recently, mathematicians and theoretical physicists have been studying Quantum Field Theory (and renormalization in particular) by means of abstract geometrical objects called motives. Amongst these ...
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1answer
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Why is Einstein gravity not renormalizable at two loops or more?
(I found this related Phys.SE post: Why is GR renormalizable to one loop?)
I want to know explicitly how it comes that Einstein-Hilbert action in 3+1 dimensions is not renormalizable at two loops or ...
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1answer
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Any link between decoherence and renormalization?
I have been studying decoherence in quantum mechanics (not in qft, and don't know how it is described there) and renormalization in QFT and statistical field theory, I found at first a similarity ...
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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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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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Why are conformal transformations so prevalent in physics?
What is it about conformal transformations that make them so widely applicable in physics?
These preserve angles, in other words directions (locally), and I can understand that might be useful. Also, ...
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1answer
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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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1answer
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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 ...
6
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1answer
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Why is $R^2$ gravity not unitary?
I have often heard that $R^2$ gravity (as studied by Stelle) is renormalisable but not unitary. My question is: what is it that causes the theory to suffer from problems with unitarity?
My naive ...
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Beta function of pure $SU(N_\text{c})$ Yang-Mills theory
What is the dependence of the beta function of pure $SU(N_\text{c})$ Yang-Mills theory on the number of colors? I guess
...
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Dimensional regularization and IR divergences and scale invariance
I want to know if dimensional regularization has any issues if the theory has IR divergences or is scale invariant.
Does dimensional regularization see "all" kinds of divergences?
I mean - what ...
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Regulator-scheme-independence in QFT
Are there general conditions (preservation of symmetries for example) under which after regularization and renormalization in a given renormalizable QFT, results obtained for physical quantities are ...
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Renormalization group evolution equations and ill-posed problems
There is a class of observables in QFT (event shapes, parton density
functions, light-cone distribution amplitudes) whose the renormalization-group
(RG) evolution takes the form of an ...
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2answers
439 views
Does perturbation theory break down for quantum gravity?
Perturbation theory presumes we have a valid family of models over some continuous (infinitely differentiable, in fact) range for some parameters, i.e. coupling constants. We have some special values ...
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Why is GR renormalizable to one loop?
I have read in a few places that GR is renormalizable at one loop. (hep-th/9809169 for example, second sentence, although they don't seem to develop this point at all). Is this do to some hidden ...
