Quantum field theory, Lecture 1

*UPDATE* Lecture notes available!
Many thanks to Dr. Alexander St. John!

This winter semester (2016-2017) I am giving a course on quantum field theory. This course is intended for theorists with familiarity with advanced quantum mechanics and statistical physics. The main objective is introduce the building blocks of quantum electrodynamics.

Here in Lecture 1 I discuss what a relativistic theory is.

[DarthCalculus]

Don't know why lectures on YouTube are more enjoyable than in a classroom. Maybe less pressure. Great teaching!

[accountone]

0:00 (Skip)
5:00 Sources and Textbooks
11:03 Outline
14:21 Notations and conventions
16:10 Theory of Everything: our higher goal
32:00 Relativistic quantum (field) theory
35:44 Poincaré group
42:55 Lorentz transformations
45:12 Poincaré group (it's a group)
49:11 Product between Poincaré transformations
54:24 Unitary and antiunitary operators

[debajyotisg]

These series of lectures is the perfect combination of board work, information, intuition and all other things that make a lecture series great.

[Lord-V]

It was at this point (and some quantum mechanics lectures) that I realised I'd never be a great physicist.
Good luck to everyone continuing in the field. I wish you the best.

[aguuaaa]

welcome to the first class.
first thing first:
lenght = time = energy ^-1 = mass^-1
D:

[sergeyliflandsky]

Regarding 59:04, separability of the Hilbert space space means that there exists a dense countable subset.
There is a theorem that says that for a separable Hilbert space there exists a basis, which means that there also exists an orthonormal basis which is a very much desired property for the framework of quantum mechanics.

[lebecccomputer]

0:00- course breakdown/university credits
14:00- notation and units
17:00- the most satisfying chalk board eraser you’ve ever seen
...to be continued

[tomasmanriquezvalenzuela]

First lecture: ~127 000 views
Second lecture: ~ 33 000 views
...
Last lecture: ~5 500 views
It's like Javier Garcia's general relativity course, first chapter ~200 000 views, but last chapter just ~7 000

[saikopatu]

I've seen and TA'd several QFT lectures in different form, but I really like your approach and will watch the whole series. Also, your jokes are hilarious. Your students must be really unfunny because I don't hear anyone laughing :D

[kevindenotaris]

When you defined a Group, you forgot to mention the associativity!

[zty]

Thank you very much for spreading the knowledge, I missed the QFT course in my school and I am glad I can catch up here!

[StinkingKevin]

I love this guy. I lecture in physiology, and I'm not bad. This guy is young, and he's making me get it. He's excellent. Fuck, yes.

[qewqeqeqwew]

Transformation with shift added to rotation isn't linear but affine. Anyway, very clean introduction, enjoyable to watch.

[vinitchauhan]

Keep up the great work :) im currently reading "An Introduction to Quantum Field Theory" by Shroeder and peskin, great book In my opinion

[shashankchandra]

What composition creates a 'quantum field' ?
Is a single quantum field a composition of 'n' number of same particles concentrated in certain 3D space around the universe or is 'quantum field' an energy concentrated in certain 3D space around the universe?
Example: is up quark-quantum field nothing but 'n' number of up quarks concentrated in certain 3D spaces around the universe and if tht particle elevates above/forward to that 3D region then it's called exictation ORRR is quantum field some type of energy(some liquid or plasma kind of) and excitations of that field is a spherical elementary particle example:QUARKS

[corbin_parker]

Maybe matter is just a form of relative energy but that’s kind of similar to string theory.

[pierrevandwalle]

Can't we just store the average data, or the refined data? Which obviate the need for infinite storage.

[mirijason]

Great lecture! I just have one question though about the positive energy condition 1:17:54 of the Hamiltonian and I hope you (or someone) will be able to answer it.

Let's suppose the universe is a closed system that is described by quantum mechanics. Then every measuring device would be described by the Schrödinger equation. Say I was able to solve it exactly (interactions and all). Then I would know the eigenstates of the Hamiltonian and these would all evolve independently just by a phase shift $\exp(-i\omega t)$. Then whatever the spectrum of H, the universe cannot decay from one eigenstate to another. Hence it shouldn't matter that the hamiltonian is bounded or not from below. The way I understand it is that it is only a problem if I am doing perturbation theory starting from an unbounded hamiltonian that I know how to solve and add interaction terms from there. But if I know how to solve the exact hamiltonian then the state of the universe could be decomposed onto energy eigenstates and each would just evolve with a phase without ever changing into other states right?

PS : and a second note - Even if my starting hamiltonian in perturbation theory is unbounded, there could exist conservation laws that would be able to prevent infinite cascading such as an electron cannot disappear and turn into a photon or whatever due to charge conservation for instance. So maybe requiring the hamiltonian to be bounded from below is not necessary after all? Just that we need to deal with all the interaction terms present non-perturbatively. I acknowledge that it may be extremely hard or even impossible to do but I believe there is a difference between our (in)ability to solve problems and the existence of solutions to them (for instance some polynomial equations of degree higher than 4 are impossible to solve using radicals although there exists solutions).

[prasadpawar]

1:16:40 Is there any reason to assume that V(t) evolves through Schrodinger equation?

[dawnwatching]

Just curious, how come this course is in English and the other ones are usually in German? Is there an expat program in the university? Great lecture, thanks for sharing!