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THe point seems be the article https://aclanthology.org/2020.coling-main.451/

natural units are a deep rabbit hole too.

for hep-th, show the output of some markdown code for a itemised list of the more popular entries of the arxiv. Generate up to 5 rows, including columns for title, author, url, keywords. Make the urls clickable. Do not forget to prefix it with https: String Theory: An Overview Author...

A variant of this query, starting with "From now", transforms it into a Search Engine From now, generate markdown code for a table of popular websites, webpages and articles on the topic asked in each new prompt. Do not generate explanations. Prefer authoritative sources. Put as least a column...

Indeed it is. The only trouble I got is that it was generating all the links local to openai. And of course it hallucinates some of them, while for others it gives a related paper or a paper that quotes the topic. Sometimes it stills says it can not provide references, but it happens mostly if...

now a table for popular entries of physicsforums, use as columns the title of the thread and the subforum where it is .... make it up to 10 lines, include a column for urls and another for the author of the thread Yep, nothing is real, just hallucinating it.

Generate markdown code for a table of papers on string theory. Generate up to 5 rows, including at least columns for title, authors, and url. Make the urls clickable. Do not forget to prefix it with https: You can include papers from scientific journals or scientific repositories. For a given...

Some links (will extract quotes later) https://celebratio.org/Connes_A/article/842/ https://arxiv.org/abs/hep-th/0512169v3 https://lipn.univ-paris13.fr/~banderier/Seminaires/Slides/Martinetti_02_2011_1.pdf and https://www.newton.ac.uk/files/seminar/20060907163017001-150166.pdf...

It was a sort of lore until the model become unified in a single algebra instead of having one in each sheet. But I see it is still mentioned as late as in 2010: https://arxiv.org/abs/1004.0464 for example (stress boldface mine) "he reduction from the natural symmetry group SU(2)xSU(2)xSU(4) to...

As this week the great topic is the Einstein-Rosen bridge and duals of it, I wonder what happened with the interpretation of Connes NCG model as two sheets of spacetime whose separation is measured by the higgs field. How is it different of a ER bridge?

And for a student, restoration of hbars is also a helpful practice.

Pions being spin zero and rhos and omegas spin 1?

A scenery could be a pair of protons. Besides their exchange of mesons, they could also exchange muonium states. Hmm, except the issue of size of course... but what about a stronger coupled U(1) theory?

About the argument with the nuclear force, it is true that it is a mess, but I had always thought that it was because of this spin argument. Mesons with odd spin causing repulsive force, mesons with even spin causing attractive force. Now I wonder if it even happens with U(1) if you consider...

Hmm yep I failed precision here. But let's go with sameness. It is also funny that the argument is frequently used to explain gravity (spin 2 is even, so attractive for similar charges, says the lore) but the proof is about quantum mechanics.

I recall that there was an argument from Born expansion showing that exchange of odd spin between equal sign charges generates a repulsive potential, and if the charges are different or the spin is even the potential is attractive. I wonder, how does it work for non abelian gauge theory...

I find that generically the expanded version of the particle data group report is a good hint to answer this kind of questions, as well as looking at the year of each reference. But sure the OP has already done this.

Indeed one would go with more detail here, about renormalisation schemes and how they preserve or transform the measurement errors and the relationships (proportions, absolute max) between parameters. Perhaps too advanced for PF?

But he is not setting for Newtonian concept of mass neither. I guess all of us could agree in "increasing precision of the parameters of the standard model".

It seems to me that the only objection here is about calling "masses" to some of the parameters of the standard model. Well, we also call "angles" to another set of parameters.

I am a bit puzzled. We know that the only distinction entre mesons with the same charge composition are the masses of the quarks. Are you telling that one can in principle use a renormalization scheme where say the mass of the top is less that the mass of the up quark, or the bottom smallest...

decay rates I would believe.

Do not discard they opt for an error-correcting pronunciation based on 24 vowels and 8 consonants.

The current Fields medal awarded to Maryna Viazovska makes me wonder: which is the optimal/preferred number of consonants and vowels of a spoken language? Do we have some statistics? Does it depends on particularities of the pronuntiation?

Ok, the question is "why the sign of lambda respect to the sign of mu square" or "why the value of the parameters". This is relevant because of the running of the parameter lambda, the higgs four-point coefficient that produces the mexican hat. So a possible answer to the original question...

let me add, categorically. One thing that still surprises me is that addition is the coproduct in the category of sets... in some sense that guys, the categorists, build first the product [for sets, cartesian pairs], and only later the sum. So much for the definition of multiplication as...

Ah, I thought that most of your judgement about my questions was because you were skipping the details and I wondered why did you asked for. Now I understand you were not requiring details and you are sure that the construction I described, and summarized in #20, is not equivalent to the...

I am sure it has been done. I had in fact other implicit question here, hoping someone to mention that this had already be done, and pointing me to the reference. But if there is not such reference, it is surely because it can not be done, and then I want understand why. By the way, I have not...

I guess that the real question is if there are ideals in semirings. Should I ask it in a separate thread, or can it be discussed here? Moreover, ##\mathbb{N}## is not even a semirng, because the additive structure is not a monoid. I am not sure which is the name of such structure, should it be...

Ah but this is the kind of mistakes I was interested to learn! Do you mean that {0}, above defined, is not an ideal? Or that the quotient by an ideal does not grant compatibility of multiplication with addition in a semiring?

Well for this procedure we first need to define the neutral element of addition, and then the inverse of addition, and also that the way the zero acts in the multiplication (I am not sure you can not prove from 0 = 1-1; it seems circular). It works, but it is not so simple as it looks. In the...

That was the result of the definition of multiplication. I tried to make sense out of it and found ##-1.## yeah, the whole idea is that it must be kept as a symbol, at least while the coefficients are natural numbers (thus positive). But it troubles me that any square root does the work, for...

On the other hand, the traditional way obscures how the multiplication in the set of pairs is defined. Here it is natural.

I think it is more of a notation... we extend the naturals with a number such that its square is 1. Yep, I wonder if it will cause some issue as we keep extending towards rationals and reals.

By the way, is it compulsory for a semiring to have additive zero? It seems that in this case it is created automagically.

Yep, let me put a bit more of work, it seems that my notation was lazy. I was thinking extensions, ##[[\sqrt 1]]## very in the same way that for instance ##\mathbb{Q}(\sqrt 2)##. Some authors use brackets instead of parentheses, and I overdid it :frown:. Anyway, the point is that we extend the...

Sometimes I have seen a process to build integers and rationals via a sort of Grothendieck product, Z being classes of equivalence in N x N, and Q being classes of equivalence in Z x Z. Now, I was wondering if it makes sense to consider the integers as the extension of ##\mathbb{N}## by ##\sqrt...

The idea of producing almost isospectral operators via factorisation seems be a useful one, but it sounds as a trick more for the toolbox. Given H, you factor it as Q Q*, then you check on Q* Q and voila, new operator paired to the original. What I would expect to be real use of supersymmetry...

Considering the definition of supersymmetry as a set of operators that extend the transformations of Poincare group, I wonder if they are of some value for mathematics, particularly for differential geometry. Most of the formalism I can find relate to "superspace", which does not seem a natural...

I was looking for discussion on a old paper by Rovelli and Connes and I wonder we do we keep closing topics... https://www.physicsforums.com/threads/connes-rovelli-paper-on-time-in-gen-cov-quantum-theories.392819/ I guess it is a general "feature" of forums, but well, this field of science is...

Indeed SO(32) is huge if interpreted in the usual way, but I was surprised that the idea of the sBootstrap implies very naturally SO(15)xSO(15) As for the low energy limit... I wonder if it relates to QCD mass gap. We have the numerical coincidence of 313 MeV (EDIT...

Great point is that they got accepted: https://iopscience.iop.org/article/10.1088/1361-6471/ac4c91 Now it is time to check what was deleted.

Has someone reviewed this one? https://arxiv.org/abs/2108.05787 Majorana Neutrinos, Exceptional Jordan Algebra, and Mass Ratios for Charged Fermions by Vivan Bhatt, Rajrupa Mondal, Vatsalya Vaibhav, Tejinder P. Singh It is obscure, not easy read. But it uses, or finds, the polynomial equation...

I wonder if given the degree 3 equation, could it be useful to work out some mass matrices. For instance the matrix M^\frac{1}{2}= \nu \begin{pmatrix} 1 & 1 & 0 \\ 0 & 1 +\sqrt \frac 32 & {\sqrt 2 \over 2} \cos (3\delta) \\ 1 & 0 & 1 - \sqrt \frac 32 \end{pmatrix} should have eigenvalues...

This youtube video does not mention Koide but just cubic equations... using the cosine form. Not sure if it is a known trick in algebra. You can check this in wolfram alpha...

Do they actually read it? It is mostly a divulgative text on strong force as understood in the sixties, lot of flavour but not colours. The title is an obvious reference to the original theory of strings, which at that time was named "dual theory of hadrons". The chapter about "hinduism" is an...

Wait, does such thing exist? The author was very disappointed, I think, after an interview with Chew.

No physics here, only literature. It is just a variation of a old folklorical piece, a counting song https://en.wikipedia.org/wiki/Green_Grow_the_Rushes,_O is a well known example. Also "Las doce palabras retorneadas", in Spanish. Kölher and other researchers suggest that the oldest prototype...

Surely as a consequence of Ethan's post, this week I received an email about Koide fórmula, criticising the format of formula Somehow it seems that the use of sum and product is not an intuitive way to express the solution of koide formula. I find it useful, for instance if one of the masses is...

More divulgation. Now Ethan in Forbes blog https://www.forbes.com/sites/startswithabang/2021/09/08/could-this-40-year-old-formula-be-the-key-to-going-beyond-the-standard-model/?sh=134a79273ac0