Tagged Questions

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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EFT and Renormalizability

Was trying to understand renormalizability in EFT. This is a little confusing especially the part of the misnomer. Can someone please explain this? Text taken from Wikipedia: "However, in an ...
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Deriving solution of the Renormalization Group Equation

I am trying to follow Matthew Schwartz's renormalization group lectures (pdf or see Chapter 23 of QFT and the SM by Matthew Schwartz), but I am having trouble with Eq. (book 23.31/pdf 29). I ...
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What does mathematical equivalence means here?

On Motls blog, http://motls.blogspot.com/2012/06/on-importance-of-conformal-field.html, while I was trying to understand what dimensional transmutation means, he said: I said that by omitting the ...
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Can you take the cutoff to infinity at a conformal fixed point?

A conformal fixed point is defined by $$\beta(g)=0$$ We hence know that couplings, masses and dimensions of operators do not flow in the effective Lagrangian when we change the renormalization ...
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Epstein-Glaser causal perturbation theory

Why does causal perturbation theory in the sense of Epstein Glaser fall under algebraic QFT rather than heuristic QFT in renormalization?
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Is gauge invariance essential to a theory be renormalizable?

Let's consider a model of New Physics in which all operator have dimension smaller than four, but which breaks explicitly $SU(2)_L$ gauge symmetry. Is this model necessarily renormalizable? ...
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Non-pertubative renormalization and correctness of a theory

Even if I start to understand why perturbative renormalization is necessary, I'm not exactly sure why non perturbative renormalization is. After asking the question to several theorists, what I think ...
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Is the exact form of the Higgs potential known?

Usually the Higgs potential is given as $$\frac{1}{2}\mu^2\phi^2 - \frac{1}{4}\lambda^2\phi^4$$ but I never quite understood if this just serves to give us an idea of how symmetry breaking works, or ...
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Why doesn't a renormalizable $\phi^4$ theory have odd diagrams?

I've been reading Zee's QFT textbook and trying to follow some lecture notes online whenever I can't grasp something. I really don't understand one thing regarding the renormalization of theories, ...
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Around fixed point of renormalization group

In the general formulation of renormalization group in "statistical mechanics" by P.K.Pathria, each point in parameter space is represented by a vector $\vec{K}$ and the transformed vector would be ...
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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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Why IR divergences cancel by cross sections of next-to-leading diagrams?

I was reading QFT & Standard Model by Schwartz, Chapter 20 which is about IR divergences. He says that IR divergences only cancel cross sections for processes involving different initial or ...
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Why don't we have logarithms or exponentials of the fields in the Lagrangians?

All tbe Lagrangian densities I have seen have always been polynomials of the fields. Is this a coincidence or is there a reason forbid, say, Lagrangians with logarithms or exponentials of the fields?
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Temperature and Renormalization Scale in QFT

A particle physicist told me that everything in Peskin & Schroder is at zero temperature, and once you consider finite-$T$ QFT, things become more complicated. Meanwhile, I sometimes see people ...
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Why is it correct to estimate divergences by the cutoff in QFT?

Let's say we have a linear divergence in a quantum field theory. The way to deal with this infinite quantum correction is to go through the whole process of renormalization. However, quite often, ...
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Anyonic braiding statistics from density matrix renormalization group (DMRG) simulations

How does the ground state energy of the system change when we braid two anyons? Can the braiding of anyons be simulated with a computational method such as the density matrix renormalization group, ...
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Charge renormalization point in massive abelian gauge theory

Let's assume massless QED. The Ward identities hold. Through this identity we determine the finite part of the counterterm when fix the value of electric charge to be the experimentally observed one: ...
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How to expand free energy of Heisenberg spin chain?

In Dasgupta & Ma's 1979 paper "Low-temperature properties of the random Heisenberg antiferromagnetic chain", they give the free energy of a few interacting Heisenberg spins on a chain. I can't ...
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Dimensional Regularization of the Higgs Mass Correction

I've found plenty of blog posts and papers where the authors claim that the Higgs mass divergence (usually presented with a momentum cutoff) doesn't show up under dimensional regularization. ...
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Charge loop corrections

Let's assume some theory in which there is some gauge group (spontaneously broken) field $B$ and fermion field $b$ which isn't charged under this group, and this statement must hold for each order of ...
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What to do when finite counterterms are undetermined?

Suppose I have some theory of "new physics" which involves interaction of some gauge boson with Standard model. For this theory I have some loop-mediated process with this new gauge boson whose matrix ...
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Pole Mass vs. Running Mass vs. Other Running Parameters

Unless I'm mistaken, physical masses that one goes out an measures in experiments corresponding to the location of poles in the propagator and such pole masses are independent of the energy scale of ...
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Experimental determination of $\Lambda_{QCD}$

I have a question about $\Lambda_{QCD}$, the energy scale at which there is a transition from the regime of perturbative QCD to quark confinement. How it is measured experimentally?
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Virtual particles and the scaling effect on valence quarks

Inside a proton there are 3 valance quarks. In addition, there is constant creation and annihilation of gluon, quarks and anti-quarks. The number of virtual particles we observe depends on how ...
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Why is tree-level interaction between neutral scalar and photons non-renormalizable?

I've read that the decay of a neutral scalar particle into two photons, i.e., $$S(p+q) \to \gamma(p) + \gamma(q)$$ can't happen via tree diagrams and instead is caused by loop diagrams (such as a ...
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How to understand singularities in physics?

The question is probably two-folded and I will try not to make it too vague, but nonetheless the question remains general. First fold: In most physical laws, that we have analytic mathematical ...
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Correlation length in d>1 Ising model, at zero temperature

I am studying the renormalization group approach to the Ising model using as a reference Cardy's book "Scaling and renormalization in statistical mechanics". I cannot understand what happens in the ...
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Momentum Space Renormalization of $\phi ^6$ Model

I'm trying to find the RG flow to lowest order in $\epsilon = 3 -d$ for the energy functional: $$f=\frac{1}{2} \phi ^2 +u \phi ^6 +\frac{c}{2} (\nabla \phi ) ^2$$ where $\ d$ is the dimension we'...
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Renormalization in Classical Field Theory

1) The statement that general relativity (GR) is not renormalizable - is it a statement only about the quantization of GR or is it non-renormalizable also as a classical field theory? 2) More ...
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Conversion of results between cutoff regularization and dimensional regularization

Generally it would be expected that a renormalizable/physical quantum field theory (QFT) would be regularization independent. For this I would first fix my regularization scheme and then compute stuff....