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12045177 No.12045177 [Reply] [Original]

Science books that filtered you

>> No.12045195
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12045195

>> No.12045224

>>12045177
>(((Science)))
Not even once.

>> No.12045869

>>12045177
Just read up some background EM/QM books and a bit of SR and you should be ready for QFT

>> No.12045877

>>12045177
How to not get filtered?

>> No.12045881

>>12045877
Have iq

>> No.12045887

>>12045881
And if one doesn't have iq?

>> No.12045888

>>12045877
qft was the first class I had to actually go through and follow the derivations or else I wouldn't understand the material.
plus it didn't help that I wasn't good with the tensor notation. is there a good resource for improving familiarity with index notation? often times I can't tell why what I'm thinking is wrong.

>> No.12045955

>>12045177
This is actually a really good new addition to the QFT texts.

>> No.12045988

>>12045887
then suffer

>> No.12046055
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12046055

>>12045988

>> No.12046766

QFT is a fucking mess. The only ones getting filtered are those who think the field is in any sense complete and consistent

>> No.12046896
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>> No.12047578

>>12046766
QFT is just a bunch of ad hoc shit that turns out to be working irl. Coming from pure maths I was shocked. Algebraic and topological methods bring some clarity and order, but they were not present when QFT was developed, ans nor are they present in typical intro courses.

>> No.12047659

>>12047578
Nobody gives a shit about those because it's literally impossible to axiomatise physics. We can't define things too formally since we don't actually know, or get to choose, how the universe is defined at a fundamental level. I do agree most physicists should learn more mathematics, but the obsession with defining things properly often just gets in the way and doesn't add much to physics.
I felt like punching this fuckwit who was clearly from pure maths who was in a lecture I was giving a few years ago and he asked me like 3 separate times whether a bunch of different shit was "well-defined"
Eventually I just had to say "yeah probably" and let him sit there fuming, but the fucking dickhead did almost exactly the same thing the next lecture.

>> No.12047676

>>12047659
> he asked me like 3 separate times whether a bunch of different shit was "well-defined"

Like he can't tell the difference between mathematically sound and observed patterns in nature.

Which is sad, because even a pure mathtard should know the limits of math

>> No.12047801

>>12045888
How the hell did you make it to qft without understanding tensor notation? Do you even understand anything you're learning?

Do you even understand why you do second quantization or do you just know how to do it?

>> No.12047810

>>12047659
>The obsession with defining things properly just gets in the way and doesn't add much to physics
QFT has been verified for the few things it can manage to calculate and in no way it is clear it can manage in a complete fundamental interactions. The lamb shift can be calculated using non relativistic QED which means it doesn't really illustrate the marriage between relativity and QM. Things like asymptotic freedom have never been described in a successful way and any problem that isn't a simplified scattering cross-section requires a bunch of patches and heuristics that are in no way contained in the general theory. So why the fuck physics texts derive shit and use terms like operators hilbert spaces and whatever if at the end they are possibly meaningless? At the end you obtain a formal result with a formal power series that yes, it surprisingly manages to give some true results but why would you trust the intuition and interpretation if they are just formal objects? How do you test the physics behind Feynman diagrams if they are just tools to compute integrals? If you actually see what sort of models are used in the LHC they are never really fully realized models of QFT and that's because full models of QFT have not been found. No the modern caveats of QFT are not equivalent to the pedantic complains of some autist if someone uses infinitesimals, infinitesimals are justified in a sense and their logical structure is sound, QFT doesn't has this nor it really is all that useful which seriously harms it's status as the most fundamental theory in physics we know.

>> No.12047837

>>12047810
as Todd Howard famously said
>all of this just works
mathlets can cope and seethe all they want. Physics isn't there to give you beautiful math or whatever. Retards who think that are stuck doing string theory and other useless bullshit.

>> No.12047838

>>12047801
I understand the notation and I understand what the stuff I'm doing is. I just have trouble in practice actually doing it once you get to more involved things. It really only shows up in derivations where there's a necessary step that involves a manipulation of the indices that I'm not immediately seeing.

>> No.12047906

>>12047837
I was pointing that QFT is not nearly as useful as usual and relativistic QM in actually giving models adn intuition and the lack of, not even rigorous, a complete mathematical treatment just goes to show that. Now the mathematical treatment of QM because of it's completion (ala dirac i.e. non rigorously) has allowed for a plethora of predictions of new phenomena that has consistently been tested. Now QFT instead of being a new complete theory like QM is, it's a bunch of results weakly related by shit like QM and Relativity that let's you predict certain phenomena that QM didn't but it actually has the same issue, the other phenomena are just assumed to be also solved by the theory because look the fine structure constant. For an important comparison, perturbation theory in QM is just a general way to approximate solutions but it is no fucking way what defines the theory nor is it impossible to write down the equations that in theory you should solve, the latter is not possible till this day in QED.

>> No.12048244

>>12047906
of course QFT isn't as useful as QM, because it's a more specialized theory. That's like complaining that hydrodynamics has less clean solutions than CM for point-like objects. The devil is in the details.

>> No.12048260

>>12047810
>>12047906
These posts indicate a real lack of understanding of QFT.
Firstly, QFT hasn't just been verified for a few things, it's been extremely successful. It's so good at describing particles that it's almost disappointing, because we hoped for some new exotic physics by now. QFT works very very well for everything not involving gravity. I don't know where you heard QFT is having issues, because the standard model is doing very well right now.
Secondly, there's no such thing as relativistic quantum mechanics without field theory. Relativity implies particle number is not conserved so any relativistic theory of particles which keeps locality intact must be a theory of fields. So those sentences make no sense to me.
Thirdly, Feynman diagrams are just quick simplifying diagrams for perturbation series. The theory was already well established before them, and you can forget about them altogether if you really wanted to. Typically students are taught something like meson scattering or a toy Yukawa model without Feynman diagrams first.
The only valid complaint here is that perturbation series do need to be replaced with some more complete description at some stage in the future.
Anything to do with formality in physics is just a waste of time though. It's fundamentally not an axiomatic thing and can't be treated that way.

>> No.12048828

>>12048260
It's been extremely successful for the things it can actually manage to calculate. And the success has to do with the precisión not with the amount of things the theory can explain. For example, there isn't till this day a complete description of the hydrogen atom with this framework (pointed by Weinberg which hasn't been solved). The reason non-relativistic QFT is still used a lot is that it actually permits computation of bound states or resonances. You can formally expose this in QFT but because you don't actually know if your Hamiltonian even exists then how the hell do you begin to treat this in a fully relativistic way? You could argue the need for QED came from spontaneous emission from atoms, and it can't handle it in the full treatment it deserves? The second case is confinement in QCD, it cannot fully explain one of the most important properties of the interaction, and what everyone believes is that it must be due to non-perturbative effects, which you cannot be sure that your theory can handle if you only have a perturbative formulation.
For your second point, this is a clear example of not knowing what the math actually implies. What it is mathematically known, is that you cannot have a Hamiltonian with causal time evolution and positive energy spectrum. Dirac's equation solves this problem by having negative energy solutions and that's it, you have a fully relativistic theory for fermions. This failed for many reasons and I agree some sort of quantization of fields is necessary but it's not that clear cut
For your third and final point, I can only say that someone must be completely unaware of the actual foundations of QFT if you don't know that people since the 1960s have tried to put the theory in a non-perturbative formulation with a complete description. The problem is not about pedantic formality, again the Hamiltonian of QED maybe doesn't even exist. That's why the yang-mills problem is a millennium problem.

>> No.12048848

>>12048244
It's not presented as such, and the consistency and applicability of the theory are highly speculated upon because it manages to explain those specialized problems.

>> No.12050054

>>12048828
Yes we know all this, but these again are not actually fundamental issues. It's well known we've been working on non perturbative approaches for a long time and it likely will need new mathematics to manage it, but there's nothing here that's actually a foundational threat to QFT as a whole.
This is all pretty well known since the fields in question on serve to define actual particle states via symmetries, but explicitly do this for non interacting particles. This is just the way the theory works, and everyone is well aware of its limits.
Besides which everyone is also very well aware of the issues Hamiltonians face even when moving to classical fields.
I don't think anyone in QFT actually sees it as a complete theory. Everyone is well aware we're still building the theory, but none of these things are crises.

>> No.12050070

>>12050054
Besides which, the Yang-Mills problem would most likely not be of interest to many theoretical physicists. Even though it's a millennium problem, we already have a bunch of ways which we generally consider as good as proof for the whole mass gap issue. This is again a bit of a disconnect between mathematicians and physicists, since physicists are generally already mostly satisfied with how this problem is answered.
The Yang-Mills problem is only going to be super important for mathematical physicists. Eventually some of the insights from the maths might trickle down to more regular use in physics but it doesn't seem super critical.

>> No.12050161

>>12048848
>It's not presented as such
by whom? A theory does not present itself. Just because high energy physics attracts pompous faggots and crackpots does not say it is somehow universal. It is only meant to describe QM in a relativistic limit, that's all. As for applicability you need to clearly define what you're talking about. The Standard Model is considered the most successful theory of the 20th century when it comes to its predictive power. The first direct evidence of non-SM behavior is neutrino oscillations, which is extremely recent (late 90s, early 00s) and we still use the same QFT methods to describe it. QFT only fails on Planck scales (extremely specific and beyond our reach) and in nuclear interactions. But QCD is extremely complicated. Similarly, just because a three-body problem can't be analytically solved in CM doesn't discredit the theory.

>> No.12050797

>>12050054
What do you understand by "foundational"? I don't understand who started this trend of trying to equate non rigorous symbolic manipulation to physics and rigorous symbolic manipulation with math. In QFT you are working with operators, hilbert spaces comutation relations, power series all of which are exploited to derive shit or build models. The foundations behind ALL of that is mathematics. If it's somewhat clear that we need new maths to actually understand what the fuck is happening that means your FOUNDATIONS are in problems. I gave those two examples as concrete issues about particular ways in which QFT has failed because I understand in physics sometimes they don't understand the role of mathematics, but if you are talling about foundations, well the problem is that the theory doesn't fucking have them. Saying "some new math" is just blind hope and not understanding the actual clusterfuck that QFT is. I belive you think this is analogous to how newton used infinitesimals, no its not because newton actually managed to give a logical and systematic way of treating basically all of mechanics, QFT doesn't have this.
>>12050070
The so called "new math" you say would basically be what this problem solves. It's not just an issue of seeing the mass gap, they are also basically asking to give full working models in 3+1 dimensions. I obviously cannot say it must be super important, but the problem was stated by Witten, not by some pure math autist. It is highly believed solving this problem could actually bring with analytical techniques to explore. Also what sort of novel logical structure are physicists using were they claim their theory predicts certain shit even though they can't actually prove it? What the fuck does it mean to convince a physicist vs convincing a mathematician? Either you are not actually using mathematics, or your shit isn't convincing. Math is grounded in a particular logical structure you cannot freely choose to ignore.

>> No.12050829

>>12050161
The reason you analogy fails os that the three body problem you can quite easily put the equations and unambiguously state with what you are working on but see there is an issue with having a solution that lets you inspect the behavior of the bodies by means of their initial data. It's kinda of a misnomer that the problem relates to knowing if a general solution exists, this was actually found by some Finnish mathematician before chaos theory and dynamical systems were a thing. The problem is that the solution is not that useful even if it is as a power series because of it's poor convergence, and that's why new techniques are preferred to have at least a qualitative idea. In QCD you can't even start with the first step I mentioned lmao, i.e. the hamiltoniann or hilbert space you are working with is not even known.

>> No.12050867

>>12050797
>Also what sort of novel logical structure are physicists using were they claim their theory predicts certain shit even though they can't actually prove it? What the fuck does it mean to convince a physicist vs convincing a mathematician?
Well standard renormalisation group methods are typically what we might reach for to convince ourselves physically that the mass gap is satisfactorily solved within QFT. If you're a string theorist, you would probably also show that it's implied through the AdS/CFT correspondence.
It's just that we don't bother with axiomatic QFT, because we need to be ready to throw away any one of these "axioms" at a moment's notice, so there's really no point. And because we have no axioms, there's no possibility of mathematical "proof". Having said that, it does accurately represent reality, so we content ourselves with that.

As for the rest, with Newton, infinitesimals, etc. No I don't think this is equivalent, and I don't really care very much to be honest. Classical mechanics is a completely different being since we can observe the macroscopic world and so axiomatising that part of physics isn't really that hard. With QFT, there's nothing. There's even fringe debate over whether locality is necessary. So of course there are no foundations we can intuit, since we aren't capable of divining the fundamental axioms of the universe.

Secondly, as for "some new maths" to describe non-perturbational methods - I was referring to how many nonlinear models can be treated exactly as of the mid-20th century, and how many were shown to have natural connections to algebraic geometry, etc. and can be exactly constructed in that way. But none of that requires much mathematical rigour, and the solution of the Yang-Mills problem isn't likely to introduce many techniques we don't know already, and is more likely to just put them on a firmer foundation for the mathematicians who worry about such things. Almost no physics is really changed by this.

>> No.12051138

>>12050829
well they're similar in that as you mentioned both require numerical methods of solution. And you can do numerical lattice QCD and get sensible results. That's all that most physicists care about, especially outside the HEP theory department.

>> No.12051673

>>12050867
Hmmm for your first point I think what I agree with is that schools like algebraic and constructive QFT have in some sense failed compared to the new techniques you mention, but I never said that in order to have proper QFT it must satisfy Wightman axioms. But renormalisation is not fully understood and till this day many physicists find it wholly unsatisfactory and it has a mathematical structure that is lacking. For example dismissing certain lagrangians based on non-renomalisability really doesn't seem to have a good theoretical basis. But I agree mathematical physicists may be chasing a red herring with traditional axiomatic QFT, still it only means we are even further from a complete theory.

>There's even fringe debate over whether locality is necessary.
This is no small thing, locality is a strong assumption that restricts the construction of many theories. Again, all of this should be included in modern research, and certainly people in mathematical physics should try to consider weakening some assumptions if there is physical justification for it. Also the axioms is not there to have a really restrictive self contained mathematical system, but more to do with why x step in QFT is valid and why y isn't. Yes obviously if your axioms deny the possibilty of using y and y seems useful and justified the problem is not with physics but with the theory, but certainly to have a rigorous and testable theory that isn't possibly unfalsifiably, you need restrictions. So yea if locality seems to imply things that go against experiment, welll obviously that means it shouldn't be an axiom.
>Yang-Mills problem isn't likely to introduce many techniques
It's literally "new math" how can it not be new techinques? The problem may be fatally flawed as I previously said, but if in any way you could make sense of what renormalization actually is I don't see why this wouldn't have massive applications. If standard arguments resist to proof, you need nonstandard ones...

>> No.12051701

>>12051138
Numerical methods are used everywhere, this is not really a problem. Lattice QCD actually has no problem with rigor, the problem is with taking limits and what things it can potentially miss by the nature of the cutoffs, and what exactly is this complete theory it approximates. Having at least a full theory, that may not be numerically that useful, but it would certainly help in showing lattice models actually approximate something. The problem of this methods is that they are not going to give you input error if the theory is not well defined, yes all the operations are well defined, but it is in no way clear what does it mean for this theory to approximate a full QCD theory.

>> No.12052067

>>12051673
I do agree with your point regarding locality issues. Personally I think the whole debate has been handled badly ever since Bohm was sort of thrown out without a fair hearing, people accepted circular proofs that hidden variables didn't exist, etc. Which is not to say I think the universe is nonlocal, but the idea is one of these things most people can't discuss fairly.
>It's literally "new math" how can it not be new techinques
Typically the mathematicians have lagged behind the physicists with actual techniques for physical problems, and so on, the most famous example I can think of off the top of my head probably being the Dirac delta.
With the solution of the Yang-Mills problem we're unlikely to get much of value because it's likely to just place stuff we already felt 99% confident in on a rigorous basis. That's not really something most people will care about very much in my opinion. We typically give informal physical reasons for why steps are valid, and that works out very well. It's often a much more effective tool than mathematical rigour. I've noticed when I give students a hard physics problem there's very little relation between mathematical ability and ability to solve the physical problem because the maths majors often just don't really know how to use physical reasoning effectively.
Having said all this, I do think there should be some closer cooperation between mathematicians and physicists. Freeman Dyson once wrote an essay on this issue that I loved. I think the problem nowadays is that for a physicist it just isn't a problem whether things are rigorous or not, and mathematicians are too concerned with rigour and stay much too distant from physical relevance. So there's a real failure to connect since neither cares about the other's goals.

>> No.12052069
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12052069

no idea what this fella was on about

>> No.12052700

>>12052069
Hannah Arendt’s pussy

>> No.12053017

>>12052067
>With the solution of the Yang-Mills problem we're unlikely to get much of value because it's likely to just place stuff we already felt 99% confident in on a rigorous basis.
Not really, there is poor theoretical understanding of QCD models at low energy regimes. This is believed to be because of many nonperturbative effects and these effects cannot be fully understood without a full nonperturbative formulation.
I think there is a big problem with how mathematical rigor is presented and why it is sometimes necessary. For example, even if Dirac's famous book wasn't "rigorous" by some standards, then why did it contain the purely formal and algebraic notion of a hilbert space? How does one develop such an abstract and weird idea? A hilbert space has little overall intuition to it and at the end you must define it through a set of axioms and then derive all the properties you need. This is what a rigorous mathematical theory does and it's what QFT tries to do. In QFT you are dealing with the quantization of classical field into operator valued fields that are also distributions, this object by it's mere definition is abstract and that's why you require all these weird formal relations to play with it. All of this is the influence of abstract mathematical thinking and it is what moves a lot of theoretical work. Yes pure mathematicians are (some, not all) not comfortable with that work because plenty of them are not interested in physics, but how on earth would all modern theoretical physicists develop all these weird tools without going into abstract mathematical subjects? There is no "physics math" and "math math" it's all math just with a different foccus. The point is that yes, rigorous abstract mathematical thinking is not a priori good for physics, but when you are dealing with mathematical objects that are abstract in nature and the intuition is no longer clear. Gauge theory requires really abstract notions of differential topology and algebra...

>> No.12053414

>>12053017
>This is believed to be because of many nonperturbative effects and these effects cannot be fully understood without a full nonperturbative formulation.
Sure but this is unlikely to be dealt with in the solution to the Yang-Mills problem. It's more likely to be dealt with by the sort of papers that gave us Lax pairs and so on, where we take the technique and throw away the rigour yet again.

>> No.12053417

>>12053414
Didn't mean to sage lol

>> No.12053418

>>12053417
it's okay, sometimes we have to fight the IQ threads

>> No.12053433

>>12053414
Yes, but the development of the technique requires rigor. This is were mathematical physics shine. Like with gauge theory

>> No.12053478

>>12053433
This is one of those questions where we'll just have to wait and see, since mathematical physics has certainly contributed to physics, but there have also been people supremely disinterested in rigour who have developed perfectly good methods for advancing physics.
I think this is particularly true with nonlinear physics where you have two almost (unfortunately) nonintersecting groups of people, one who worked directly on how these techniques work in physics and others showing their connections to algebraic geometry.
I would like closer communication and cooperation again but we'll have to see how it goes in the end.