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Thank you Reggid. Is this consistent with what Orodruin writes above - ie what we're measuring when we measure this 'running mass' is something different from the mass of bottom quark itself?

Thank you Orodruin. I thought the pole mass was just the mass of the *free* particle in its own frame -- which is why, given confinement, the pole mass isn't well-defined for quarks. And I thought that the 'running' mass of the particle was its effective mass when undergoing interactions at...

Hi everyone, I understand that the phenomenon of running charge predicted by QFT has been experimentally verified: the physical charge on an electron really does vary with the energy at which it is measured. I have two questions: (1) Does anyone know what the canonical experiments confirming...

Thanks for the video! What a great resource.

I have read many times that a theory (such as gravity) that contains couplings with negative mass dimensions cannot be asymptotically free. Does anyone have a reference that proves that that's the case? The argument is usually just that the coupling grows with energy, as seen in the...

that's a really wonderful answer. Thank you! Going to try and digest it a bit, and get back... But thanks so much!

Hi all -- can anyone offer a qualitative explanation of why it is that couplings run with the energy in *relativistic* quantum theory, and not in non-relativistic? Some insight here would be much appreciated. Thanks.

Thank you, The_Duck. A final question: it seems strange to me that a particle can undergo an interaction without some interaction property to couple to. (In the case of real interacting theories, for example, we have properties like charge, color, and weak isospin in addition to their...

I'm looking at the simplest example of an interacting theory, and this is the theory of a neutral scalar boson $\phi$ with $\lambda \phi^4$ interaction term. Can I ask: is there a physical interpretation of the `charge' through which this field interacts with itself? In particular, is \lambda...

Thanks a lot. I appreciate that of course we can't measure an electron in the absence of interactions, but I'm wondering if it even makes theoretical sense to ascribe a charge to a field occurring in a free theory. Of course there will be a global U(1) charge in this case, but it seems to me...

The question is in the title: is it possible for a theory to be both UV and IR stable? And concrete models would be much appreciated!

Sure -- but then we talk about 'the charge on a free electron' all the time, and I'm wondering how this is defined. Maybe another way to ask the question is this: given that we take QFT to admit free-field models, are any of these models in which electrons have charge? Here's why I'm...

The_Duck, Susskind discusses mass renormalization in a way that aims to be intuitive here: . (In case that's of interest!)

Hi there, I have a question about the definition of a charge of a free electron. Let's suppose that QED is the true theory of the interactions of charged particles. Presumably the charge on an (effectively) free electron, then, is the charge on an electron in which the electromagnetic...

Thank you very much TheDuck. A final question. You phrased your claim regarding the physicality of running couplings in terms of alpha, the charge parameter. But just to confirm, would you regard the running of mass as as 'real' as the running of charge? Thanks again though -- really...

Thank you very much The_Duck. That's tremendously useful. One last thing (if you're still around!). At times you make it sound as if the mass 'running' is just an artefact of the renormalization scheme. However, am I right in thinking that we have actually measured that the masses (sometimes...

Thank you! First, just to clarify: Depending on what renormalization scheme you use, the 'bare mass' is thought of as either infinite or the measured mass of an electron. So I take it you must have the latter scheme in mind, is that right? So now two questions: (1) Is the mass of the...

Hi there, I have a question about the rest mass of an electron. As we all know, the charge of an electron is a function of the energy at which the system is probed. When defining the charge, we typically use as our reference scale the charge measured in Thompson scattering at the orders of...

Hi folks -- it is my understanding that only non-Abelian gauge theories can be asymptotically free. But can anyone provide me with a canonical reference showing that such symmetries can be dynamically broken and still retain that status? I gather that this is the case (from reading the...

Weird question, but does anyone have any feelings on whether parity can be classified as a kinematic property? It doesn't scale with energy and so in that sense doesn't seem to be classifiable as a dynamic property, nor do objects interact through it; but parity is of course violated by the...

Thanks, The_Duck. Fascinating!

That's great people: I think I know the Susskind lecture and I'll watch it again. Final question. Does anyone know of a place where a conjectured Lagrangian for a QFT of gravity is written down? I would like to see how the mass 'couplings' that occur in, say, the Standard Model relate to the...

Thanks very much: of course that's the answer. But may I ask one more thing. All the parameters appearing in the Lagrangian are interaction couplings, with the exception of from mass. Is there a reason that mass is singled out in this way? Is there perhaps some reason that we can think of it...

I have a question on quantities that 'run' under the renormalization group flow. What's clear is that the properties through which particles couple -- such as charge, isospin, color etc -- change in their strengths as the energy increases. But this running is also true of the mass, which is a...

thank you very much, that is tremendously helpful!

Hi folks -- does anyone know of a good survey article on the topic of whether local gauge invariance is a requirement of a fundamental theory within QFT -- hence of an asymptotically safe theory? I only have a few scattered remarks to this effect (by F. Wilczek mostly), so any good...

I just received this in an email from a rather famous physicist whose name I'd rather not mention. "The classic Montonen-Olive duality of N=4 super-Yang Mills illustrates both self- and non-self duality. For gauge group SU(n) or SO(2n) the dual theory is the same, but the paper Gauge...

OK: so is the idea here that the Callen-Symanzik equation governs renormalized coupling constants, and those things are only introduced in order to deal with divergent diagrams, which always include loops (and hence are intrinsically QMical)? Thanks for reminding me of the analogy with...

Yes, I appreciate that the running couplings appear in QFT. But -- as anyone who's benefited from reading Feynman knows -- derivation is not always the same thing as explanation. Is there a story, a gloss we can give on why the running of couplings is *distinctively* quantum?

As is well known, the charges through which particles interact scale with the energy in QFT. What I was wondering is: can we say that this is a peculiarly 'quantum' phenomenon (or maybe, quantum-relativistic)? Is there a reason why it wouldn't be the case in a classical universe, for example...

Hi folks, I just read a passage by the great Ashoke Sen in which he writes that, due to the possibility of particle production in collisions, "strictly speaking there is no experiment possible even in principle that can distinguish elementary from composite particles." But how is this...

Hi folks, I am looking a bit at the phenomenon of S-duality (as a bit of an amateur) and looking at the literature I am getting mixed messages concerning whether or not N=4 supersymmetric Yang-Mills theories are in general self-dual. Does anyone happen to know anything about this?! I'd...

I am new to QFT and found myself wondering the following. Particle physics experiments usually consist of looking at what happens when we smash two protons together. As such, we look to calculate amplitudes for 2-> n scattering, with n the number of particles that emerge from the other side...

I have a couple of questions about entanglement and decoherence! 1. Sometimes you read that, strictly speaking, all electrons are entangled with one another. But can that be right?! Isn't it at least the case that electrons have to have interacted with one another in the past in order to...

Hi folks: I have a question on dualities. Does anyone know of a QFT with a (conjectured) S-duality, such that the two classical theories corresponding to that QFT have very different Lagrangians? That is, such that the two classical theories that define the QFT cannot be expressed as...

Hi folks, I'm assured that scattering cross-sections in QFT computed at tree level correspond to cross-sections in the classical theory. For example the tree level cross-section for electron-electron scaterring in QED corresponds to scattering of classical point charges. But I'm not sure I...

Thank you very much! So appreciated. :)

Strangerep, do you have the section ref for Weinberg? I can't seem to find thie discussion of this. Thanks mate!

Hi folks, I've been reading about Montonen-Olive duality and understand that two different classical theories can give rise to the same QFT. In particular, we can have a classical theory of electrically charged particles giving rise to a magnetic monopole, and a classical theory of magnetic...

Hi folks -- does anyone know of a proof that particle (quanta) number in QFT is / is not Lorentz invariant? I'd be happy to hear of it -- so thanks!

Hi folks -- I have three questions on Montonen-Olive duality. This duality switches the electric and magnetic couplings, where these couplings are related by the Dirac quantization condition eg = 2\hbar\pin Here e is the electric charge and g the magnetic (monopole) charge. 1. First of...

Hi folks, I have been trying to get my head around dualities, and hit a stumbling block right away. Duality hypotheses are framed by thinking about perturbative expansions of interaction lagrangians ( at least when thinking about s-dualities). In such expansions, the first term is regarded as...

Take a look at this: http://arxiv.org/abs/1308.5599

Atyy, thank you very much for your answer and for the reference to the OS conditions. I have one more question in case you happen to know the answer to this too. In the Feynman approach, we feed in a classical action in order to calculate outcomes of quantum field-theoretic processes. Is...

Hi All, In the Feynman, 'sum over paths' approach to quantum field theory, we compute amplitudes, generating functionals etc by feeding in a "classical action". By calling the Lagrangian that we feed in "classical", this mean that the fields that feature in that action are regarded as...

Hi folks -- could anyone think of a justification of the idea that if a function's arguments diverge (i.e. are taken to infinity), there's a high probability that the function too will diverge? This would be really helpful for thinking about fundamental theories in particle physics, so any...

Hi folks -- I was reading some (non-technical) work by Frank Wilczek, in which he stated that any fundamental theory -- that is, well behaved in the E →∞ limit -- must be a local gauge theory. Does anyone know of the reasons for why this is thought to be the case? Even sketchy remarks...

Hi folks -- quick question. I appreciate that entangled states in quantum mechanics may not be bound states. But when we have bound states, are the particles always entangled with one another? Thanks a lot!

thank you -- that'll do nicely. much obliged.

I don't have library access at the moment. I studied PP about 10 years ago and just want to look at some wavefunctions to make a point about composition.