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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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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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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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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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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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 ...
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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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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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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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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 ...
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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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Why do string theory and Hopf algebra renormalization seem to have no intersection?

Hopf algebra appears in recent papers that systematize renormalization of quantum field theory (QFT). For example see Connes' work and citing papers or a paper referenced here on PSE: R. E. ...
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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 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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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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Why is $\rho_m$ proportional to the deviation from critical temperature in critical phenomena?

In Peskin and Schroeder's chapter 12 about the renormalization group, it is stated that the parameter $\rho_m=m^2/M^2$, where $m$ is the mass and $M$ is the renormalization scale, is proportional to ...
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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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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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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 ...