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3 votes
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Schrödinger equation, 2D delta function potential, and confusion

Congratulations! You (probably) just stumbled for the first time in your life with the fine art of regularization and renormalization, the craft of making sense and getting rid of infinities in ...
Gabriel Ybarra Marcaida's user avatar
2 votes
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Why do we rescale momenta after integrating out high momenta in Wilsonian renormalization?

OP wrote: However doesn't the rescaling (12.19) undo getting rid of all momentum modes $\Lambda' < |k| < \Lambda$, since the path integral will now include momenta in this range? No, the ...
Qmechanic's user avatar
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2 votes

Some integrals in QED Renormalisation

Your suspicion is justified. You are indeed missing a crucial approximation not mentioned in your post, turning a simple few-line calculation into an exercise in self-torture. The photon mass $m_\...
Hyperon's user avatar
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1 vote

Some integrals in QED Renormalisation

Your complaint is not entirely justified, the first integrand is just a rational function, for which solution methods can easily be found: integration-rational-functions Although tedious, it can be ...
Jos Bergervoet's user avatar
0 votes

Renormalizability of Quantum Gravity

Well, Griffiths is seemingly equating gauge theory with Yang-Mills theory, but there are many other types of gauge theories, cf. e.g. this and this Phys.SE posts. Concerning non-renormalizability of ...
Qmechanic's user avatar
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1 vote
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Derivative interactions in the Wilsonian renormalisation Group

I will try to answer your questions one by one. Please comment if you need any clarifications. Before I do that, let me briefly review the idea of RG flow which might make the answers to (1) and (2) ...
Nandagopal Manoj's user avatar
1 vote

What is the physical meaning of the counterterms we add in Lagrangians?

There are two answers to this depending on what you mean. Based on your question it seems both levels of understanding would be useful. The second answer actually has more of a "physical meaning&...
JohnA.'s user avatar
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1 vote
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Renormalization group equation, the Callan-Symanzik equation, and renormalization group flow

You must stick to your QFT text, or, if confusing, to Chapter 19 of From Classical to Quantum Fields, by L Baulieu, J Iliopoulos, & R Seneor, (2017, Oxford University Press) . What is the ...
Cosmas Zachos's user avatar
1 vote
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Is the magnitude of the $\beta$ function important?

The sign of the β function is only more meaningful than its magnitude in crude qualitative arguments of the schematic asymptotic behavior of couplings—a speculative theorist's dream. In real-life ...
Cosmas Zachos's user avatar
3 votes

Renormalisation in quantum optics

In quantum optics, the calculations usually only involve tree level diagrams, which does not require renormalisation. Such calculations are only relevant when considering nonlinear interactions. In ...
flippiefanus's user avatar
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1 vote
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Problem solving for Wilsonian Effective Action

I haven't checked the details of your integrals, but assuming that that's all done correctly, the only thing you're missing is log rules and a series expansion. Using $a_i$ to mean the corresponding ...
Rokas Veitas's user avatar
1 vote
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Why do correlation functions involving composite fields require special analysis?

As already pointed out by @Prahar, the problem of the definition of a composite operator arises already in the free theory. Considering the Lagrangian of a free real scalar field, $$\mathcal{L}[\...
Hyperon's user avatar
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2 votes

How do we know at the operator-level that the tadpole $\langle\Omega|\phi(x)|\Omega\rangle=0$ vanishes in scalar $\phi^4$ theory?

I think you are basically there: Let $\hat{U}$ be the unitary operation you defined, $\hat{U} \hat{\phi}(x) \hat{U}^\dagger \equiv -\hat{\phi}(x)$. This is a definition. We then assume (or check) that ...
Lucas Baldo's user avatar
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1 vote

Difference between renormalizable and super-renormalizable theories

Qmechanic's answer is very good and tackles your main question well. I want to however add an important detail to your first question. Namely, we generally do not just consider $[\lambda]$ when ...
mika's user avatar
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3 votes
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Triviality of $\phi^4$ theory, is it settled now (2024)?

It sort of depends on what exactly you mean by "settled". Up to physics standards, the question is definitely settled: it has been understood, for many decades now, that $\phi^4$ in $d=4$ is ...
AccidentalFourierTransform's user avatar
2 votes

Triviality of $\phi^4$ theory, is it settled now (2024)?

Currently, the question in $D=4$ is settled by this paper of Michael Aizenman and Hugo Duminil-Copin.
Jon's user avatar
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2 votes

Triviality of $\phi^4$ theory, is it settled now (2024)?

It is settled now, $\phi^4$-theory is indeed quantum trivial in 4 spacetime dimensions. In 4 spacetime dimensions, a series of papers by Luscher and Weisz demonstrated early numerical evidence (by ...
QCD_IS_GOOD's user avatar
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3 votes
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Difference between renormalizable and super-renormalizable theories

It should stressed be that Peskin & Schroeder are here using the old Dyson definitions of renormalizability. For a more general derivation of eq. (10.13), see e.g. this Phys.SE post, which also ...
Qmechanic's user avatar
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0 votes

Question about RG from QFT perspective, in particular Weinbergs book

Lets take for example QED. We know we need to include renormalization constants on the gauge field $A_\mu$, mass of the fermions $m$, the fermion field $\psi$, and the coupling constant $e\rightarrow ...
MathZilla's user avatar
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0 votes

Is RG fixed point always related to a second-order phase transition?

For starters, fixed points need not to be critical points, they can also correspond to phases. For example, in the Ising model case there are fixed points at $T=\infty$ and $T=0$, corresponding to the ...
Jun_Gitef17's user avatar
1 vote
Accepted

Why is $\frac{1}{2}\delta_Z(\partial_\mu \phi_r)^2 - \frac{1}{2}\delta_m \phi_r^2$ treated together in Feynman diagrams?

Why are these two terms treated as one You don't have to treat them as a single contribution. It is perfectly acceptable to consider two different vertices with factors of $ip^2\delta_Z$ and $-i\...
SolubleFish's user avatar
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