I dont get why you do not lose generality when you assume that your hilbert space is a function of the same manifold that generates the symmetries. It is not the case when your hilbert space is defined on Euclidean or minkowski space, if I am not wrong. Do these results generalize to that?

Why is the character of an inverse element equal to the complex conjugate of the element's character?

Maybe a very stupid question but I’m confused. From about 53:00: If |v>+ = <v|, why is in the definition of the inner product <v| the column vector and not the row vector? I briefly had a moment of "aaah, that's where it comes from!", shortly followed by "wait..." 😅

i typed eqft gerwgrewreggrwergwsSWEGR in the search bar what am i doing here

@ 0:27 HE IS SO RIGHT ON THIS. THE "THEORY" ITSELF IS NOTHING BUT A MATHEMATICAL INTELLIGENCE TEST.

Thank you for the lectures; concise, clear and a great way to start learning CFT as a beginner!

Thank you for the lecture! I have the following question in regards to the definition of the equivalence class [|psi>] of a vector |psi> ( 1:05:44 ). You defined it as all vectors that differ only by phase. This makes sense, since 2 quantum states are identical if they differ only in phase. But since the Hilbert space contains more vectors than those with norm 1(normed states), then the logical thing is to define the conjugacy classes of the Hilbert space as the rays in it, i.e. [|psi>] := {z |psi> | for all z in C and z not 0}. This way we get a one-to-one correspondence between a state and a conjugacy class. So, shouldn't [|psi>] := {z |psi> | for all z in C and z not 0} and not [|psi>] := {z |psi> | for all z in C such that |z|=1}?

This professor is such a bore to watch, a gravitational personality.

Great! Q: You say the proof you showed *only works for locally unbiased estimators*. And at 47:15 you avoid saying var(A) could become the MSE for a biased estimator, as it seems it should be. Did you exclude that possibility on purpose because of *...*?

Very clean green boards

Vielen Dank Herr Osborne fürs Video

Thanks, Professor Osborne, for the great lecture! I really liked it. Just a quick thought: maybe for those long theorems, it might be helpful to have them displayed on a screen instead of writing them out. A lot of work to write them down.

Thank you

At 52:00 you write \lambda > 0. But imposing \Omega(X) > 0 for scaling gives us \lambda > -1/2.

Dear Prof. Osborne, how can I assist the last lecture? Thank you in advance

Hallo Herr Osborne, Beispiel am Ende der Vorlesung: muss c2 nicht -1/⍺^2 sein? und die Gleichung entsprechend c1 + ⍺c2=0?

Can we speak about a differentiable function whithout the two notions of vector space and norm on it...

Very nice lecture. I would just like to make a suggestion. I think the example you used of Z2 to explain why every group can be interpreted as a permutation (i. e. as a subgroup of the permutatiom group Sn) is far too trivial... a more complex example would be much more interesting and iluminating (for starters, you used the only example where Sn is the same size as the group you want to represent, which is bascially never the case). For those struggling with this point, the key idea to understand why every group element can be represented as a permutation of the group elements is this. Consider an ordered list of all group elements. Now act on all elements of this list with one of the group elements (say g) from the left. You will get all the group elements again, and each one will appear only once, but the list will be in a different order (the fact that you will get all elements of the group and everyone of them only once follows from the group axioms; its not an immediate obvious fact but its not hard to understand why it has to be so). This means that acting on this list with the group element g is equivalent to performing a permutation of the group elements. This is valid for all group elements, so thats why you can always identify a group of n elements with a subgroup of Sn.

Hall Thomas Hall Gary Anderson Edward

in 39:10, shouldn't f(α) = -2Nt|α|^2+NJ|α|^4-μN|α|^2? Edit: nevermind it gets corrected later on in the lecture at 53:03

Hallo Mr. Osborne, schöne Vorlesung, da jedoch nicht alle Teile aufgezeichnet wurden, möchte ich gerne wissen, ob die Möglichkeit besteht, das Skript als pdf zu bekommen. Herzlichen Dank im Voraus

Sehr geehrter Herr Prof. Dr. Osborne, vielen Dank für Ihre Vorlesungen. Mir helfen diese wirklich sehr weiter! Ich hätte eine Frage an Sie bezüglich des Ausdruckes bei der partiellen Integration der Delta-Funktion. Ich habe diesbezüglich glaube ich gerade einen Denkfehler. Ich kann mir leider gerade nicht erklären wieso der zweite Term dort nicht mehr von H abhängt, sondern nur von der Ableitung unserer Funktion f und diese dann nach x wird. Ich dachte zunächst, dass Sie als Integrationsgrenzen vielleicht 0 und plus unendlich gewählt haben und für diesen Bereich ist H=1 und Sie diese deswegen nicht mitgeschrieben haben, aber ich glaube, dass die Grenzen immer noch bei plus und minus unendlich liegen und ich deswegen einen Denkfehler haben müsste. Könnten Sie mir bitte helfen diesen Schritt besser nachvollziehen zu können? Ich wünsche Ihnen einen angenehmen Abend! Mit freundliche Grüßen

Thank you for the great lecture! By any chance do you have the previous (first?) lecture recorded?

Thank you!

Thank you!

What is the next lecture course going to be? Do you take requests haha?

Picture an infinite fundamental particle static to the CMB. It’s infinitely small and infinitely expressed. Every universe expresses this particle infinitely. Each infinitely expressed particle expresses every matter, force, field, and everything else humans don’t know about are expressed probability wise infinitely. It’s simply probability that lets us experience them. Duh

I feel like everything you are writing on the board is basic quantum mechanics sense. Yawn

Bruh… when do you get to the cool part? lol

There is something about Noether's theorem that has always bothered me. There are two common derivations of it. One derivation is this one, and the other is where you make the parameters of the transformation spacetime-dependent (it's in the yellow CFT book). Usually I would just say well there's just two derivations, multiple ways to do the same problem, but they appear so superficially different that I'm left wondering if they actually are different. Do they prove slightly different statements? Is one easier to generalize to other situations? I honestly don't know.

I think if you include the singular points you get a different quantum theory. Why do we choose to exclude the singular points, especially when for bosons it seems they should be included?

Hello Professor Osborne, I want to thank you for uploading all these videos. They have helped me a lot, mainly because you very much know how to communicate your knowledge and how to connect the material to other areas, fields and to research. You show your students the bird's eye view making everything so much clearer. Thank you!

Sir can you recommend a resource ot read about circulant matrices in this qft context ? I cant find any at all, only you have mentioned this . Thank you sir

Quantum symptom looks at electrical (r/c/e) the formula for quantum soup theory

Hallo Herr Osborne, Vielen Dank für Ihre Videos. Ich sehe mir Ihre Videos gerne an und habe eine Frage: Am Anfang (bei Minute ca. 13 berechnen Sie das Volumenintegral des Quaders zu 1/8. Wie ist das zu interpretieren, wenn doch ein orthogonaler Quader mit Kantenlänge 1 ein Volumen von 1 hat ? Ich vermute, dass die Funktion T(x*y*z) gar kein Quader, sondern ein dreidimensionales Dreieck darstellt, oder ?

ja Mir vasic verstundeb aber licht vous schhemical stalbelisim,

Warum so mysteriös? Ein Massepunkt ist der Massenmittelpunkt dem die gesamte Masse zugeschrieben wird. Vgl. KZbin VL Universität Wien Physik, playlist Physik I Müsste ca. 8.Vido sein. Trotzdem gutes Video 👍

10:25 "These prerequisites are vital. I would suggest you pause the video right now and make sure you're familiar with these things". Proceeds to pause the video and realize: not familiar with these things. ... Unpauses and keeps watching.

Sir you are giving wonderful lectures, its very helpful. Just a request you can please not waste water for just rubbing board, you can use dry cloth. I think letters on board will still be visible. Thank you

Thanks a lot, sir for such a nice lecture. I am a PhD math student with a research interest in cosmology. I would like to know what software you use to record both the screen and your video because my friend and I also make lecture videos on topics like Topology, Riemannian geometry, Measure theory, etc.

if symplectic geometry is not great for noisy systems, what approach should I use instead.

Excellent lecture content.....your students might "hate" your bias for using the subtle historical concepts but it complete and thought provoking. Might be useful after going through the normal lectures with bells and whistles BUT still find them lacking on BASICS and Overview. Its a struggle to look up the basics concepts. Same genre as this lecturer : Universität Wien Physik by Prof Dr.Ing : Paul Wagner (I learnt much from him and his style of teaching without and hand waving ; i was amused when he loses his "cool" when students do not get his messages but he recollects himself and re-explains using another approach ). BRAVO Herr Osborne

Very very profound statement at 3.0 : Hypothesis has not been rejected......probably influenced due to your stay In Deutshland..Ja

Best lectures on Quantum Field Theory on the internet for mathematically minded people. Love from Pakistan

Hello Prof. Osborne, thanks for the lectures! Could you please give me the reference to the paper you mention at 49:53 in the lecture?

Thank you so much for these lectures! Very well chosen topics, the explanations were clear and the pacing was perfect.

Thank you for the great lecture! The 2 step drying chalkboard is very refreshing aswell, also the sunlight is very thematic 🙂

من فضلكم كيف اترجم الفيديو الئ العربية؟

I have neutrino flavor theories in my profile. Last four uploads. Last two are hand drawings to explain gist of it, but other two I use perplexity ai to express mathematically. Im messaging all mathematicians to get everyone involved in this kind of approach