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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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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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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Why do we expect our theories to be independent of cutoffs?

Final edit: I think I pretty much understand now (touch wood)! But there's one thing I don't get. What's the physical reason for expecting the correlation functions to be independent of the cutoff? ...
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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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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 ...
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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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Divergent sum in lightcone quantization of bosonic string theory

I had the following question regarding lightcone quantization of bosonic strings - The normal ordering requirement of quantization gives us this infinite sum $\sum_{n=1}^\infty n$. This is regularized ...
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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 regard - after my ...
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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 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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How does the sum of the series “1 + 2 + 3 + 4 + 5 + 6…” to infinity = “-1/12”? [duplicate]

How does the sum of the series “1 + 2 + 3 + 4 + 5 + 6…” to infinity = “-1/12”, in the context of physics? I heard Lawrence Krauss say this once during a debate with Hamza Tzortzis ...
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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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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 does it mean for a QFT to not be well-defined?

It is usually said that QED, for instance, is not a well-defined QFT. It has to be embedded or completed in order to make it consistent. Most of these arguments amount to using the renormalization ...
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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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Is there a non-perturbative remormalization? If so, how does it work?

Is there a method to renormalize a theory without using perturbative expansions for the divergences? For example, is there a method to get masses and other renormalized quantities without using ...
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Is QCD free from all divergences?

On page 8 in http://arxiv.org/pdf/hep-th/9704139v1.pdf David Gross makes the following comment: "This theory [QCD] has no ultraviolet divergences at all. The local (bare) coupling vanishes, and the ...
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What is the difference between pole and running mass?

For example, when we meassure Higgs boson mass to be 125 GeV, do we think about renormalized or pole mass? Should the mass of the Higgs change if it is produced at higher energies?
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What exactly is regularization in QFT?

The question. Does there exist a mathematicaly precise, commonly accepted definition of the term "regularization procedure" in perturbative quantum field theory? If so, what is it? Motivation and ...
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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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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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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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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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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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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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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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Basic question about the S-Matrix, Unitarity and Effective Field Theory

Consider scattering some particles in a state collectively denoted by $i$ to a final state denote by $f$. The scattering amplitude, S-matrix is then defined by: $S_{fi}\equiv \langle ...
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Quantum field theories with asymptotic freedom

QCD is the best-known example of theories with negtive beta function, i.e., coupling constant decreases when increasing energy scale. I have two questions about it: (1) Are there other theories with ...
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Evaluating propagator without the epsilon trick

Consider the Klein–Gordon equation and its propagator: $$G(x,y) = \frac{1}{(2\pi)^4}\int d^4 p \frac{e^{-i p.(x-y)}}{p^2 - m^2} \; .$$ I'd like to see a method of evaluating explicit form of $G$ ...
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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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Divergent Series

Why is it that divergent series make sense? Specifically, by basic calculus a sum such as $1 - 1 + 1 ...$ describes a divergent series (where divergent := non-convergent sequence of partial sums) ...
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Why is renormalization necessary in finite theories?

Michael Brown made the following comment here: The modern understanding of renormalization (due to Kadanoff, Wilson and others) is hardly controversial and has nothing really to do with ...
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Instantons and Borel Resummation

As explained in Weinberg's The Quantum Theory of Fields, Volume 2, Chapter 20.7 Renormalons, instantons are a known source of poles in the Borel transform of the perturbative series. These poles are ...
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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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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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Dimensional regularization: removing more than just logarithmic divergencies?

I have followed two courses on QFT, which both involved renormalization by dimensional regularization. My confusion is that one of the professors claimed that dimensional regularization can only be ...
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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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Renormalization of field strength

I'm revisiting the elementary algorithms of renormalization that are taught in a classroom setting and find that the procedure taught to students is as follows: Write down the bare Lagrangian: ...
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Semantic problem about renormalizability

This post relates to this previous one. My question is, what is the actual meaning of a theory being renormalizable? There might be at-least two possibilities (correct me if I am wrong) ...
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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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Under what conditions are the renormalization group equations “reversible”?

As I understand it, the renormalization group is only a semi-group because the coarse graining part of a renormalization step consisting of Summing / integrating over the small scales (coarse ...
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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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Divergent bare parameters/couplings: what is the physical meaning of it? Do this have any relation with wilson's renormalization group approach?

I understand that bare parameters in the Lagrangian are different from the physical one that you measure in an experiment. I'm wondering if the fact that they are divergent has any physical meaning? ...
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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 ...
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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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LSZ reduction theorem derivation in Weinberg QFT

When deriving LSZ reduction theorem Weinberg in his QFT book have assumed n-point generalized Green functions, $$ G(q_{1},...,q_{n}) = \int d^{4}x_{1}...d^{4}x_{n}e^{-i\prod_{i =1}^{n}q_{j}x_{j}} ...
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A certain regularization and renormalization scheme

In a certain lecture of Witten's about some QFT in $1+1$ dimensions, I came across these two statements of regularization and renormalization, which I could not prove, (1) $\int ^\Lambda \frac{d^2 ...
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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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Defining a CFT using beta-functions

Won't it be correct to define a CFT as a QFT such that the beta-function of all the couplings vanish? But couldn't it be possible that the beta-function of a dimensionful coupling vanishes but it ...
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Can we obtain non-Lorentzian metric from Lorentzian metric, through renormalization methods?

Since low-energy, non-relativistic thermal field theories are defined in Euclidean spacetime, while high-energy relativistic theories are define in Minkowski spacetime, I was wondering if there are ...