# Questions tagged [renormalization]

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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### What is the Wilsonian definition of renormalizability?

In chapter 23.6, Schwartz's quantum field theory book defines renormalizability as follows, paraphrasing a bit for brevity: Consider a given subset $S$ of the operators and its complement $\bar{S}$....
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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 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? I....
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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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### 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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### 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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### 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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### What is precisely the energy scale of a process?

Coupling constants run with the energy scale $\mu$. But what is exactly this energy scale. My question is, if I have a physical process, how do I compute $\mu$?
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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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### 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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In standard (non-Wilsonian) renormalization we split the bare Lagrangian $\mathcal{L}_0$ into a physical Lagrangian $\mathcal{L}_p$ with measurable couplings and masses counterterms $\mathcal{L}_{... 6answers 2k views ### Why Does Renormalized Perturbation Theory Work? I've read about renormalization of$\phi^4$theory, ie.$\mathcal{L}=\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-m^2\phi^2-\frac{\lambda}{4!}\phi^4\,,$particularly from Ryder's book. But I am ... 1answer 5k views ### What does it mean to integrate out fields from a theory? I've done a fair bit of reading on this subject and I'm still confused about the basic principle of integrating out fields in QFT. When we have a function of 2 fields a and b, f(a,b), and we integrate ... 1answer 786 views ### Why does local gauge invariance suggest renormalizability? I'm reading Gauge Field Theories: An Introduction with Applications by Mike Guidry and this particular remark is not obvious to me: A tempting avenue is suggested by the QED paradigm, for if a ... 1answer 522 views ### Why do we need to prove the gauge invariance of QED (or all of the gauge theories) on the Feynman diagrams language? Let's have the QED lagrangian. It has explicit gauge invariance, so, by the naive thinking, all of the EM processes must satisfy the property of gauge invariance. So why do we need to recheck of gauge ... 2answers 1k views ### What is wrong with a nonrenormalizable theory? Non-renormalizable theories, when regarded as an effective field theory below a cut-off$\Lambda$, is perfectly meaningful field theory. This is because non-renormalizable operators can be induced in ... 1answer 867 views ### Why Zeta regularization is not valid for multiple-loops? Why zeta regularization only valid at one-loop? I mean there are zeta regularizations for multiple zeta sums. Also we could use the zeta regularization iteratively on each variable to obtain finite ... 2answers 6k views ### How does the sum of the series “1 + 2 + 3 + 4 + 5 + 6…” to infinity = “-1/12”? [duplicate] How does the sum of the series “1 + 2 + 3 + 4 + 5 + 6…” to infinity = “-1/12”, in the context of physics? I heard Lawrence Krauss say this once during a debate with Hamza Tzortzis (http://youtu.be/... 2answers 413 views ### What do we mean when we say 't Hooft proved that Standard Model is renormalizable? This question is inspired from Why should the Standard Model be renormalizable? Ron Maimon says that standard model is renormalizable, and though there seems to be conflicting (?) answers. Is this ... 1answer 583 views ### Where does the delta of zero$\delta(0)$come from? It is common when evaluating the partition function for a$O(N)$non-linear sigma model to enforce the confinement to the$N$-sphere with a delta functional, so that $$Z ~=~ \int d[\pi] d[\sigma] ~ \... 1answer 969 views ### Scalar Yukawa theory Let's consider the theory given by the following lagrangian$$ \mathcal{L} = \frac{1}{2}\partial_\mu\phi \partial^\mu \phi - \frac{1}{2} M^2 \phi^2 + \bar\psi (i\gamma^\mu\partial_\mu - m)\psi + \frac{... 2answers 687 views ### Renormalized mass I am reading Schwarz QFT and I reached the mass renormalization part. So he introduces, after renormalization, a physical mass, defined as the pole of the renormalized propagator, and a renormalized ... 5answers 4k views ### 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 ... 7answers 2k views ### Dirac once said that renormalization is just a stop gap procedure, and there had to occur a fundamental change in our ideas. Did something change? Once, Dirac said the following about renormalization in Quantum Field Theory (look here, for example): Renormalization is just a stop-gap procedure. There must be some fundamental change in our ... 2answers 4k views ### In what sense is the renormalization group equation a group? The renormalization group equation is given by: \begin{equation} \left[\mu \frac{\partial}{\partial \mu} + \beta \frac{\partial}{\partial g} + m \gamma_{m^2} \frac{\partial}{\partial m} - n \gamma_d \... 2answers 2k views ### What is the connection between Conformal Field Theory and Renormalization group in QFT? As I know, the fundamental concept of QFT is Renormalization Group and RG flow. It is defined by making 2 steps: We introduce cutting-off and then integrating over "fast" fields$\widetilde{\phi}$, ... 1answer 1k views ### Which values of the Riemann zeta function at negative arguments come up in physics? For my bachelor's thesis, I am investigating Divergent Series. Apart from the mathematical theory behind them (which I find fascinating), I am also interested in their applications in physics. ... 3answers 752 views ### 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:$${\... 7answers 2k views ### 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 ... 2answers 2k views ### 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) but,...
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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) 1.Power-...
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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 ...