Spinors for Beginners 21: Introduction to Quantum Field Theory from the ground up

[@eigenchris]

This post will contain some errors, and also some notes from my friend who studied particle physics: ERRORS: - 7:30, the mass term on the left-hand side should be (mc)^2. I forgot the c. c=1 is only true in natural units. (thanks to @dylanledermann8629) - 41:09 the upper index of J should be nu (v). Similarly at 41:33 for B. (thanks to @pieterkok7486) - Throughout the video I got the sign wrong on the Faraday tensor. It should be "F^uv = ∂^u A^v - ∂^v A^u" defined with a minus sign, since F is an anti-symmetric tensor (thanks to @codetoil for pointing out the timestamps 39:11 39:16 39:39 42:20 42:40 1:30:19) - 1:15:08 not exactly an error, but the momentum conjugate to Φ(k) is really ∂_tΦ†(k) = ∂_tΦ(-k). (You can check this yourself by applying the conjugate momentum formula to the Lagrangian density L = (∂_tΦ† ∂_tΦ)/2 - (m+k)(Φ†Φ)/2, and you'll get ) So I really should have calculated the commutator as [Φ(k), ∂_tΦ(-k~)] = δ(k-k~) instead. This gives the more "familiar" minus sign instead of a plus sign. NOTES: - Condensed matter physics and particle physics are basically the same theories, but at low and high energies. Complex scalar fields describe both phonons (sound particles in condensed matter) and the Higgs field in particle physics. Both topics are taught in the same chapter of Lancaster and Blundell's "Quantum Field Theory for the Gifted Amateur" - In my "QFT cube" at 4:50, the "field theory" corner can be thought of as enforcing "locality"... i.e. effects in physics are due to immediate surroundings, and there is no "action at a distance". Feynman talks about this in his 1986 Dirac Memorial Lecture: www.cambridge.org/core/books/elementary-particles-and-the-laws-of-physics/the-reason-for-antiparticles/9D72E7C9045A9C0797DD952678F03C75 - 52:55 worth noting that the time-dependent schrodinger equation for 1 particle is the non-relativistic limit of the Klein-Gordon equation (you can take this limit by taking c->infniity) - 1:10:12 the "mass relation" I talk about here is usually called the "dispersion relation" in the context of waves. - 1:20:47 the "infinite ground state energy" is related to the non-zero ground state energy of the standard quantum harmonic oscillator shown at 36:10 - 1:21:50 the space here where we create and destroy particles in a field (or lattice) is called "Fock space"

[@AsrafAli-bq5ww]

41:09 the upper index should be nu (v), but, is not it a dummy index?

[@codetoil]

The formulas for the Classical/Quantum Maxwell/Proca fields in potential formulism should result in an antisymmetric tensor (you should be subtracting the terms, not adding them) 39:11 39:16 39:39 42:20 42:40 1:30:19

[@eigenchris]

@@codetoil oops. That's definitely a blunder. Thanks for pointing that out. I added it to the list.

[@swarupdas1857]

Pppppppppp

[@franks.6547]

14:43 "arbitrarily" setting kappa = m in order to obtain a constant propagation velocity c, because we want to model that for Lorentz invariance. It is a weird additional constraint - the more inertia, the more rigid - in order to make the relativistic target equation (KG) resemble somewhat a sheet of coupled oscillators. But in the end, it's not coupled oscillators at all, and the particle restmass m~ is per definition the energy it takes to create a static field elongation psi without further interactions (free field)

[@timuralmabetov2213]

I truly don't know how to express my gratitude for your tremendous effort in sharing this wonderful knowledge with us. Thank you very much!

[@TheBelrick]

And thank goodness for the standard model of physics, cosmology and of course quantum physics. Thanks to these advances, I have been able to throw out my old electro-magnetism based, classical physics derived, microwaves, and tv's and cellphones etc. Replaced by the technology derived from post 1927 copenhagen conference physics and cosmology. Why just the other day I peered through my quantum telescope and saw a 13billion old universe newly formed from big bang, compressed into a much smaller universe. Glimpsed darkmatter and turned off gravity at all. Gee thanks mathmagicians! The impact your scientism has had on all our lives is telling.

[@antoniojpan]

I have just left a tip in the link at the description

[@scienceclick9092]

The greatest playlist of all time

[@dyachenkotimofey6682]

I would be so happy, if you would continue with QFT or even make a whole playlist out of it, because you are the best source, that no book or professor can beat by how well you explain everything!

[@parreiraleonardo4189]

This is better than Netflix!

[@weirdcreatures4985]

You're Amazing. That's what actual science is! We don't memorize stuff, we understand it. You're doing an excellent job and I don't have words to express my gratitude to you. May you achieve whatever you desire!

[@cademosley4886]

Congrats on finally making it to the Big Time! We're all on this ride with you.

[@Untoldanimations]

What a time to be alive. Next semester I am tutoring an undergrad class in particle physics and the prof has given me zero direction. I will definitely be rewatching the series to brush up on QFT. Much love

[@pacotaco1246]

We are all winors. Glad more people are going to learn some QFT from this series!

[@taibilimunduan]

an excellent overview of advanced physics in a single video

[@Duskull666]

Just in time for my QFT 1 test, hurray! ❤

[@dzuchun]

every time I feel tired of physics and want to finally get it out of my life, someone like you comes along and magically prevents that (not mad at all, thank you! ❤)

[@jeremybrennan8473]

THEY TURNED ME INTO AN OPERATOR MORTYYYYYYYY

[@dng88]

Very excellent summary. Totally agreed about the witchcraft comment - if x is inf x -x is not 0 but inf still ! Hence the potential is only relative is a good stopgap argument but not maths. Totally witchcraft.

[@nice3294]

Probably the most illuminating video on this topic I've seen, great work!

[@hiiamhiggs9660]

I really need to finish your Tensor calculus series to start the Spinors for beginnors series! Its unbelievable how someone who at one point in his life didnt even know what the inertia tensor is, managed to become the best physics education source on yt. Lots of gratitude from germany.

[@narfwhals7843]

I agree that Quantum Sense's playlist is great and approachable. But for a more in depth introduction to mathematically rigorous quantum mechanics I recommend Professor M Does Physics. Their videos go into much more detail on the derivations and cover everything from Dirac Notation to the Hydrogen Atom.

[@antoniojpan]

Simply: wonderful. You have been able to organize and summarize my 4 years long travel into physics. You have a great ability to explain. I feel like if you read my mind, and just filled the gaps I had. Thank you.

[@Globbo_The_Glob]

Unbelievably pumped up to study this. Your videos have a really incredible explaniative power, because you don't skimp on the details but respect their insights.

[@Globbo_The_Glob]

To follow up, I think you are uniquely placed after this series to deep dive gauge theory. As someone interested in this topic, I find it difficult to find anything to explore that is not brutally simple or impenetrable without 6 years of work. I understand it's a tricky topic, but there is a lack of intermediate content. If anyone reading this has resources, please, into the bowl below x

[@georgesas7090]

Superb video as always! I very much appreciate the way you go through things stressing the concepts more than the maths, while not compromising the latter. This is exactly what is missing in most textbooks and classes.

[@shafiulhossain6270]

You are the best. Thanks so much for your videos. I watched most of them, and they helped me a lot.

[@kikivoorburg]

Very excited!! Thanks for all your wonderful work!

[@keksleckerlecker]

This is some real good content right here. The explanations are amazing! Please continue this series :)

[@EccentricTuber]

It's finally out! Congrats and thanks!

[@IronAsclepius]

I've been waiting years for this. Very excited, thank you!

[@giuliocasa1304]

Thank you very much! I've just discovered this interesting playlist about theoretical physics and I'm following you: again thanks for sharing!

[@Tymon0000]

Obligatory "Spinors for Beginnors" comment

[@ProfessorBeautiful]

This video is an outstanding achievement and contribution. Thank you!

[@edd.]

What an incredible, simplistic breakdown of QFT. I cannot wait for the next few on the Dirac equation!🤜🤛

[@sarkknuckle6029]

great addition to this amazing series, learnt so many useful things and tools to look into the physical world in a more appreciable way. Loved your exterior algebra video, and this one is so useful to me as I begin my QFT course (more of self-learning). Would love to know what content or books you took note from for this video.

[@eigenchris]

I'd read parts of "No Nonsense Introduction to Quantum Field Theory", and "Quantum Field Theory for the Gifted Amateur". However a lot of the stuff with coupled quantum oscillators and fourier transforms I had to put together from stuff found on google and a little bit of me just figuring things out.

[@sarkknuckle6029]

@@eigenchris Thanks for the reply, and I do realize lot of things I learn eventually comes from online stuffs. Your video series being a big example. Hoping to see more great content from you

[@edd.]

Woohoo🎉🎉🎉. What a surprise!!! I’m on this!!

[@erikstephens6370]

1:20:26-1:20:50, I actually think there's a very reasonable explanation for this infinity: ordering ambiguity of the ø and π terms in classical mechanics. The first thing to note is that between classical and quantum mechanics, quantum mechanics is the more fundamental theorem, meaning we can derive classical physics from it, but not vice versa. The second thing to note is that the terms representing operators commute in the classical theory. this means that one could start with the Hamiltonian (π^2)/2+(ø^2)/2+(∂ø*∂ø)/2 and add a commutator like [ø,π]=øπ-πø and the classical Hamiltonian wouldn't change, as the ø and π values commute in classical field theory. In quantum mechanics, however, adding this commutator would result in a completely different operator as the ø and π quantum operators no longer commute. This ability to add what is essentially zero in the form of a commutator in classical mechanics means that we have an ordering ambiguity. Putting this together, we are essentially working backwards when starting from classical mechanics and "deriving" the quantum version of each Hamiltonian, making an educated guess as to what the quantum version is, based on the classical result. However, to find the right hamiltonian, we have to resolve the ordering ambiguity. These infinite shifts in the vacuum energy happen whenever we pick the wrong ordering of the Hamiltonian's operators. To make a coherent quantum version of the Hamiltonian, we pick the ordering that results in all the creation operators being to the left of the annihilation ones, resulting in a vacuum-state energy expectation value of zero (All energies are relative to the vacuum state, so might as well let the vacuum state energy be zero). At least, this is what I've come up with, working on understanding this theory. All that really matters is that our choice of a quantum Hamiltonian leads to the correct classical version, up to some re-ordering of the terms. As long as we start with the normal ordered quantum Hamiltonian, we get a sensible vacuum-state energy, and we can recover the classical Hamiltonian, plus/minus some commutators (which vanish in the classical theory), by substituting the a/a† operators in terms of ø and π. It's all down to ordering ambiguity in the classical theory.

[@erikstephens6370]

Still not sure about the renormalization for Feynmann diagrams with loops in them, though. I don't quite understand those diverging quantities.

[@bjornfeuerbacher5514]

@@erikstephens6370 These divergencies are commonly interpreted as due to the fact that we include arbitrarily large energies and momenta in the integrals, whereas in reality, the quantum field theories we have are actually only correct up to a certain energy range.

[@erikstephens6370]

@@bjornfeuerbacher5514 The loop integral ones? or the normal ordering ones?

[@bjornfeuerbacher5514]

@@erikstephens6370 The loop integral ones.

[@erikstephens6370]

@@bjornfeuerbacher5514 I see. Thanks.

[@abdatmohammed5112]

this man need a noble prize ❤💫

[@MissPiggyM976]

Simply the best, keep on please!

[@freniisammii]

YOOOOOOO LET'S GOOOOOOOOOOOOOO!!!!!!!!!!! 3 days before my birthday todayyyy.

[@mehmetalivat]

Thank you for this course. This is so appreciated.

[@crochou8173]

sakurai served me well for the prerequisites

[@erdnaelarresaccor3450]

Sakurai is the goat

[@Wielorybkek]

wow, what a ride, that was so good

[@utof]

when it comes to getting the intuition behind the mathphys subjects, im starting to trust eigenchris on a dangerously high level i dont mind it tho :-)

[@AMADEOSAM]

Very very useful! Many thanks for all your work. I hope you can make some lessons on QFT using path integrals.

[@pieterkok7486]

Thanks for the great video. Minor typo at 41:09 - the (upper) index of J should be nu (v). Similarly at 41:33 for B.

[@eletronica_do_airton]

Thank you.

[@ShadowZZZ]

Awesome video! I love it

[@vkoptchev]

At 14:53 any insight why kappa is set equal to m (mc^2 actually to preserve dimensions)? These are independent parameters, what motivates this constraint? Thank you for all your videos!

[@eigenchris]

I don't have a specific physical motivation for it. Mathematically, it's what you need to do if you want a field that is Lorent-invariant and is consistent with special relativity. It puts the time derivative and space derivative terms on equal footing.

[@willemesterhuyse2547]

Timestep: 56:05. I see you couple each point to a spring, but then you couple the other side of the springs to a physical substrate. This substrate don't necessarily exist in a row of points of a quantum field.

[@willemesterhuyse2547]

Timestep: 15:40: Can you substitute d_mu phi^i with a temporary variable "y" for computation purposes or do you have to substitute by a (1, 1)-tensor y_mu^i.

[@eigenchris]

The index "i" on phi is just for countinf the number of fields you have. If you only have 1 field, you can ignore the index. But if you have 3 fields, you will have 3 separate equations of motion from 3 seaprate Euler-Lagrange equations.

[@FacultyofKhan]

One thing I’ve always wanted to see explained intuitively is the path integral: I was wondering if you had plans on taking that route! I also realize that you’ve mentioned before that you’re going to take a break after finishing this spinor series, but I’m curious if you’ve thought of going further into the QFT rabbit hole!

[@Arevilov3]

No way, you're here too! I learnt tensor calc from your channel 😁

[@edd.]

I hope so!! There are a lot of tunnels down they rabbit hole to take!

[@emmabrenchuk144]

Physics with Eliot has a video introducing the Path Integrals intuitively

[@eigenchris]

At this point I don't plan on making a video for path integrals or QFT in general. For one thing I don't understand either of them particularly well, so I don't really have many intuitive explanations under my belt yet. QFT is also a huge topic and I'm not sure I have the energy to both learn it and explain it properly. I imagine if I was to make a video on the path integral, I would start with the path integral approach for the ordinary 1-particle Schrodinger equation (standard quantum mechanics, no QFT), and then see how it could be generalized to QFT. Chapter 6 of Sredniki covers the standard QM path integral without QFT. I tend to try start with examples that are "as simple as possible", which is why I spend so much time on the coupled oscillators in this video.

[@lanimulrepus]

Excellent!

[@hellfirebb]

Hi chris, would you explain why the combination of of x and p operator (two observables) gives creation/annihilation operators(which sounds like not observables at all, but mutating/altering the system instead)?

[@eigenchris]

I don't know the physical reason. I just know that'a now the math works out for the quantum harmonic oscillator. I skipped the proofs of showing those operators raise and lower energy levels, but there are other youtube videos that cover them.

[@hellfirebb]

@eigenchris Thanks and let me check out the other sources that talk about them. Btw just a quick check, are the ladder operators still hermitian operators (or unitary, or may be not even either hermitian or unitary)?

[@AH-ju5jx]

Hi Chris, thanks for the brilliant series of tensors! I was very confused with regard to why the order of the summation signs can be flipped. I have been imagining the summation as a formation tree as used in logic, no textbook on matrices explains this either, they just say refer to Fubini's theorem. But where can I find the proof? Like say there is a tensor with 20 covariant and contravariant components each now I change the order of the summation sign of of 3 of those components and yet the summation stays the same? How should I prove this? By mathematical induction?

[@eigenchris]

I'm just thinking intuitively... let'a say you had 2 summations with 3 indices each. If you write every single term explicitly, you would get 9 terms. You could group the terms into groups of 3 based on either the first summation index oe the 2nd summation index, but the result is still the same 9 terms. I assume you could prove the general case by induction after you prove a base case.

[@AH-ju5jx]

Thanks again!

[@willemesterhuyse2547]

Timestep 57:53: I see distribution does not work as usual on tensor products of states. Is this an error or is it true? Doesn't this lead to inconsistencies?

[@eigenchris]

Can you specify which line you're talking about? I'm not sure what you mean.

[@willemesterhuyse2547]

@@eigenchris Going back from line 4 to line 3 on right side.

[@eigenchris]

@@willemesterhuyse2547 Line 3 to 4 is just the operators acting on their respective vectors. Line 4 to 5 is a standard property of the tensor product. a(U⊗V) = (aU)⊗V = U⊗(aV). If you think of U as a column and V as a row, this makes sense.

[@dylanledermann8629]

At 7:30, you said the spacetime interval for 4-momentum is equal to mass but there should be a c for the speed of light since you also divide the time-component of 4-momentum which is energy by c so clearly, we're not using natural units here. That means, the spacetime invariant is m*c

[@eigenchris]

Yeah, my bad. I was switching in and out of natural units at various places in this video and that's a mistake.

[@HalKworasmi]

Around 40:00, I think you misswrote - by + in both thé proca équation and thé Maxwell one.

[@eigenchris]

Yeah, I made that unfortunate copy+paste mistake throughout the video. I made a note in a pinned comment about it.

[@abdatmohammed5112]

we are waiting for the next video please don't be late ❤❤❤❤❤❤❤❤❤❤❤

[@ShadowZZZ]

I don't get how at 1:11:20 you're saying that the normal mode coefficients are exp(-ikx) ? Given that in the last slide before, you said that \phi(x)_k = A(k)*exp(-ikx), so wouln't that mean that, for big Phi, we just do the integral over k of just phi? Wasn't the A(k)'s the coefficients? It just makes no sense to me if you're saying that the phi^hat is the same as the phi_k in the last slide... It seems like you're relabeling the solution field-pos. wave (e^-ikx) as the amplitude, and the A(k) as the phi^hat field-pos. operator. I'm confused

[@abdatmohammed5112]

please we need an episode about the quantazition of the three fields, dirac maxwell and klein gordon

[@geoffreyfaust3443]

At around 55:06, would this non-conservation argument relate to virtual particles, or is this already subsumed somewhere in the equation through some representation of Heisenberg uncertainty?

[@eigenchris]

I'm not sure what "non-conservation argument" you're talking about at 55:06. Is that the right timestamp? I'm not at the point where I confidently understand virtual particles. But so far, I understand them to correspond to "internal" lines in Feynman diagrams like the ones seen at 1:34:29. Any line that "enters" or "exits" the diagram will have a well-defined momentum we can measure. But when you have internal loops, you can assign any value of momentum to the internal lines, as long as you "give it back again" so that the momentum of the external lines doesn't change. I'm not sure if I consider "virtual particles" to be a real physical phenomenon at this point. They might just be a calculation trick. But again, I'm not well-versed in this topic.

[@geoffreyfaust3443]

@@eigenchris Thank you for the reply. By non-conservation argument, I meant something that I understood you (perhaps erroneously) to be saying: that QM had to give way to QFT, in part because QM assumes that you have the same number of particles throughout the time period of measurement. However, beta decay of 1 neutron into 1 proton, 1 electron and 1 antineutrino contradicts this assumption, as one particle turns into three. So I was asking whether virtual particles might also add to this particle counting inequality. However, if you don't believe in virtual particles, then I guess it's a moot point. Thanks again.

[@tomgraupner171]

Wonderful work ! Again ! Please allow one question: The idea that QFT is related to Harmonic Osciallators (HO) sounds weird to me. HO do not travel, but waves do. HO solutions are Hermite Polynomials, while QFT solutions are complex sinusoids. HO need a force/potential to work, QFT-fields do not. Is this "HO thingy" just a "close but no cigar"-picture, which should help beginners to get a rough idea? Or do I miss the point? Anyway: Thanks a lot for your video. It's a very good introduction !

[@eigenchris]

Like I say in the view, a (scalar) quantum field can just be thought of as a bunch of quantum oscillators joined together. If you prefer: a quantum oscillator is a quantum field with zero space dimensions (you shrink the x,y,z axes of the field to length zero so that you only have a single point where the single HO lives). I would imagine that the wavefunction solutions for 2 coupled oscillators would involve Hermite Polynomials in some way, but I'm not sure how. You would need to generalize them to polynomials with 2 variables. A quantum field would have wavefunction(al) solutions that are the extension of the Hermite Polynomials for an infinite number of variables. But that's hard to deal with. So just as with the HO, we switch to the raising/lowering operator representation to make things easier, we also switch to the raising/lowering operator representation to make things easier in QFT. The "sinusoidal" solutions in QFT aren't wavefunction(al) solutions--they are just ways to write operators that correspond to creating a particle state with a specific momentum... similar to how you can climb up the energy ladder of a HO using operators without worrying about the wavefunction. The mass term in QFT can be thought of as equivalent to a potential term in the HO. They play the same role. I'm still a beginning in QFT to some extent, but this is how I view quantum fields. I view the HO interpretation is correct, not a "close but no cigar" picture.

[@tomgraupner171]

@@eigenchris Thanks a lot for these explainations.

[@Kraflyn]

super awesome!

[@autumrnk]

We're eating good tonight

[@AsrafAli-bq5ww]

Awesome chris, are you planning to make the mathematics behind Feynman Diagram in the future videos?

[@eigenchris]

I don't plan on it, honestly.

[@Thatcher_Lai]

Thanks a lot for your video and spinors series. I have a question though. I've watched Quantum Sense's video on generators and he showed that the time derivative of the Lagrangian L is negative that of energy E. He then said energy pushes time forward because of this and then showed how to get H = -ihbar d/dt. But how or why can we take this "leap of faith"? As in, why can we say that because dL/dt = -dE/dt, therefore Hhat psi = ihbar d/dt psi and hence hamiltonian causes time evolution, where he said L is analogous to psi since they both represent the state of a system? I get how adding hbar makes the units correct and how adding i makes it hermitian, but it still seems a bit random to me. Is there any intuition behind this? It might just be me being dense. Thanks for your help.

[@eigenchris]

I don't really have a great answer to that, unfortunately. It is indeed a "leap of faith" from my point of view, but it's a leap of faith that seems to consistently work. "Canonical quantization" is the process of replacing Poisson Brackets from Hamiltonian mechanics with Commutators, and that seems to consistently work for developing quantum theories. If there's a deeper reason for why this works, I don't know what it is. You'll have to google or ask elsewhere to find out.

[@abshark]

Christmas came early 🎉

[@onebronx]

eigenchristmas

[@marisbaier6686]

@29:36 shouldn‘t it be abs(psi)^2 instead of ||^2? Because then the (…)^2 ist doubled

[@eigenchris]

If the magnitude is 1, the square doesn't matter anyway.

[@marisbaier6686]

@eigenchris absolutely brilliant video btw!!! Some parts give an amazing recap and the new parts blow my mind away!!

[@pmadjidi]

i wanted to implement numerical methods to solve for some basic Feynman diagrams, looks like there is a lot more to it then i expected....

[@eigenchris]

Yeah, they are fairly complicated. I don't know much about numerical integration, but my guess is you'd want to find a text that teaches the techniques for how Fenyman diagrams are computed numerically.

[@alexgoldhaber1786]

Valuable content. The numbering of episodes is confusing though; 21 came after 22. I'm a physicist there's no loss of continuity for me but 'aesthetically' 22 should come after 21 😂😂

[@drdca8263]

Despite doing work with infinite volume limits of quantum spin systems (I.e. where you have a lattice of sites, each of which has a spin, and it is a quantum mechanical system), I have still felt pretty confused about what kind of mathematical object a quantum field is supposed to be. This video seems to make it clear enough to me: A quantum field is (pretty much) a family of observables indexed by positions in space (or, err, maybe an operator valued measure where if integrated over a region of space it is an observable? whatever) (or, the Fourier transform of that same thing, if you want it indexed by momentum instead), and where these correspond to the field strengths in a classical field theory. It kind of makes me wonder what I was so confused about? And so, thank you very much, this really clarified things for me!

[@eigenchris]

I read the "A No-Nonsense Introduction to Quantum Field Theory" textbook and came out of it still not really knowing what a quantum field was. The idea that the Schrodinger Equation still applies in QFT also seems to be a detail a lot of sources ignore. I don't think I really understood them until I made this video. I mostly view it as just the extension of the coupled quantum oscillators, with the continuous limit taken so that the oscillators are infinitely close together.

[@throwaway1369]

We're back

[@Eric-u3v3r]

HI. Can you make a video about page-wootters mechanism

[@eigenchris]

Sorry, I don't know what that is.

[@hiiamhiggs9660]

Algorithm comment !!!

[@simonkay6533]

Lovely!

[@ElFazo]

Thanks

[@f_add_mebowshot5677]

After 5 min I came to the horrifying realization that this video would have to end somewhen but then saw that I still got 90min to go🎉🎉🎉❤

[@freniisammii]

I'm curious, are you ever going to do a serious/research into string theory?

[@eigenchris]

Don't think so. I don't even really understand QFT, and that's a prerequisite for string theory.

[@freniisammii]

@eigenchris ah, ok. Sorry if this is a little preemptive then but do you have any lecture series planned, or subjects you want to dive into after this one?

[@eigenchris]

@@freniisammii Honestly, no. I'm not sure I plan on doing any more series in the near future. I might just do one-off videos on things that interest me now and then.

[@My.KS_1806]

Can u explain fourier tranform theoretically??

[@eigenchris]

I don't plan on doing a video for that. You'll have to look at another channel. Maybe 3blue1brown?

[@ericvilas]

I think you have an error in the Proca equation- shouldn't it be a minus sign instead of a plus sign? like, d mu A nu - d nu A mu, so it matches the Faraday tensor

[@edd.]

Might depend on whether he used the contravariant or covariant form.

[@gabitheancient7664]

I'm not quite understanding what is a 1-particle state here, since there is one 1-particle state with localized position and another with localized momentum how would be a generic 1-particle state be defined? what even is a particle? is it related to the previous energy eigenstates?

[@eigenchris]

There isn't really such a thing as a "generic 1-particle state" in QFT. Quantum fields are taken to be the fundamental entity that exists. Particles are viewed as the various possible "excitations" of quantum fields. You can work with either particle position states or particle momentum states depending on the type of problem you're dealing with. Most of the time in particle physics, you are tracking particle interactions/"collisions", so momentum states are usually used.

[@gabitheancient7664]

@@eigenchris holy shit weird but that makes sense tbh someone else in a discord server explained that particles are in general a quanta of a certain spectrum of the system, so yeah in that case a position or momentum quanta but hooly shit that's so cool too

[@Swaroque]

It's nothing weird if you've studied Fourier Analysis and Quantum Mechanics. QFT is not a joke, first master Quantum Mechanics then come to QFT.

[@gabitheancient7664]

@@Swaroque I know what a fourier transform is I was just confused why these were both called "1-particle states" if they are different types of excitations in the field

[@muonneutrino_]

This playlist is my roman empire

[@Moshe_Sellam]

😍😍😍

[@mathoph26]

I do not agree: relativistic QFT proposes only single particles lagrangian with "interaction models"... the theory to be complete should propose many body lagrangian with properly defined relativistic potential interaction (including correlation!). So what you say, hides a lot of issues.

[@pendalink]

yesssss

[@idegteke]

How the level of complexity changes on the axis of size then again? Because currently the minimum point is arguably at the atomic size scale. Smaller as well as larger formations start to be very obviously much more complex. Have any of you ever given this FUNDAMENTAL fact a minute of honest consideration?

[@Kraflyn]

aren't all feynman diagrams singular? Not just the closed loops ones.... The Klein-Gordon Green function itself is singular, and diagrams perturb it. Hence the +ik trick in the numerator.

[@eigenchris]

I'm not an expert on Feynman diagram. I know the problem with loop diagrams is that they allow for a variable momentum on some of the internal lines, and so (in theory) you need to integrate over all possible momenta for -ve to +ve infinity, which is what causes divergences. These are fundamentally different than any problems you encounter with no-loop diagrams.

[@Kraflyn]

​@@eigenchris On page 2: sgovindarajan.wdfiles.com/local--files/serc2009/greenfunction.pdf All Green functions are singualr in QFT and relativisticQM. Dirac, Proca, Klein. Some can be "re-normalized" by the +i epsilon trick to integrate in the complex plane around the singularities, poles being artificially removed. These are called "well behaved integrals", even though all of them are singular. The problem with loops is - they cannot be solved using the usual tricks of regularization. You encountered one in this video: the dirac delta at the origin, the sum of all the ground states for all the particles quantum oscillators. Schwinger "regularized" it by cutting it off at the pair production energy 2m, again, artificially, and then sold the fiction of those interactions not happening because it is not the same graph any more. But this happens to the newly formed graphs too. Then, Casimir encountered vacuum energy too as the sum of all naturals n. He then interpreted this as the Riemann Zeta at s=-1, which it is not, since the Zeta defining series converges absolutely only for s>1. It is a mess. Something is wrong in the entire theory. And no one cares to notice anything. The integrals diverge properly to infinity, all of them. One can renormalize them any way one likes. Any result can follow from this. And so we pick the result that agrees with observations. We cheat. Peeps call it "the most precise theory ever"! :D Someone should address this finally, this is going on since the fine structure result some century ago or so. It's a disaster. And it is not solely due to QFT, it appears in rudimentary results too, without fields and quantum oscillator models. All of us should look into it. Yes, Feynman was a fraud, a cheat. Physics today is an american bloated bubble of jokes. And it starts to show slowly: proton structure, muonium, both of these experimental results do not agree with the theory. The discrepancy isn't large, but it is at 5 sigma, so it is relevant. Someone should address this asap. Like, a century ago if possible :D Repeating nonsense makes no service to science unfortunately. Regards.

[@Kraflyn]

@@eigenchris On page 2: sgovindarajan.wdfiles.com/local--files/serc2009/greenfunction.pdf All Green functions are singualr in QFT and relativisticQM. Dirac, Proca, Klein. Some can be "re-normalized" by the +i epsilon trick to integrate in the complex plane around the singularities, poles being artificially removed. These are called "well behaved integrals", even though all of them are singular. The problem with loops is - they cannot be solved using the usual tricks of regularization. You encountered one in this video: the dirac delta at the origin, the sum of all the ground states for all the particles quantum oscillators. Schwinger "regularized" it by cutting it off at the pair production energy 2m, again, artificially, and then sold the fiction of those interactions not happening because it is not the same graph any more. But this happens to the newly formed graphs too. Then, Casimir encountered vacuum energy too as the sum of all naturals n. He then interpreted this as the Riemann Zeta at s=-1, which it is not, since the Zeta defining series converges absolutely only for s>1. It is a mess. Something is wrong in the entire theory. And no one cares to notice anything. The integrals diverge properly to infinity, all of them. One can renormalize them any way one likes. Any result can follow from this. And so we pick the result that agrees with observations. We cheat. Peeps call it "the most precise theory ever"! :D Someone should address this finally, this is going on since the fine structure result some century ago or so. It's a disaster. And it is not solely due to QFT, it appears in rudimentary results too, without fields and quantum oscillator models. All of us should look into it. Yes, Feynman was a fraud, a cheat. Physics today is an american bloated bubble of jokes. And it starts to show slowly: proton structure, muonium, both of these experimental results do not agree with the theory. The discrepancy isn't large, but it is at 5 sigma, so it is relevant. Someone should address this asap. Like, a century ago if possible :D Repeating nonsense makes no service to science unfortunately. Regards. Oh, please do continue making these, they are awesome! Simple and to the point! Please do continue

[@greenguo1424]

Chris-tmas came early this year

[@miguelaphan58]

Waooooooo!!!

[@kellyaquinastom]

Spinor Drop

[@RobertLeitz]

Here is one of the "End Points".. Where is "The Green" in "The SpaceX Launch"...???... "Google A Rainbow Picture"...Take Care...Bye... Look at "The Rainbow" as "A Gentle Pendulum Clock"... Green Arrow In Or Down.. Orange Arrow Up Or Out.... "Yellow Is The Tick".... SpaceX Launch Speeds Up The Pendulum.... "Squeezes The Rainbow Together"... Green Goes "In" The Engine.. You Can Only See Orange "Out".. Take Care...Bye... "Mechanically"..??... Green = BTDC...Yellow = TDC..Orange = ATDC.. The Rainbow Fires On All 3... But when you "Speed Up The Fire Engine"..??.. You can only see it firing on 2..Yellow/Orange.... That's why you won't see Green...??... In a "Fast High Energy Release"..... Take Care...Bye...

[@evilotis01]

oh shiiiiiiiiiit

[@kukproject]

私が生まれた理由

[@NovaWarrior77]

You know so much it’s disturbing

[@jasonwilkes9383]

Anyone December 2024?

[@joelsepicvids]

No I'm still November :(

[@joshi8218]

You sound depressed mate

[@umbraemilitos]

He's just monotone, but honestly I like it as a style. You can speed up the video if you want the pitch to change.