Symmetries and quantum mechanics: basics, Wigner's theorem, linear representations of groups

In this short lecture series we will learn the basics of the representation theory of groups in the context of quantum mechanics. The first lecture is focussed on interpreting the word "symmetry" in QM, and relating them to linear representations of groups. Problem sheets will not be distributed.

[@hakimben8054]

Welcome Back, Professor Tobias Osborne.

[@jonlasa9034]

Really waiting for the next video!! Thank you very much for your insights in group representations, super useful!! 🎉

[@hakimben8054]

Thank You so Much for this useful lecture, Professor.

[@javierrendon2194]

We missed you

[@mfourn97]

He is BACK 😍

[@conorosirideain5512]

He's back 🎉🎉🎉🎉

[@Anonymous-kj6cu]

Thank you, professor.

[@aboubacarnibirantiza4748]

Thank you professor for the Wonderful course
Can I get the basic book on symmetries and quantum mechanics

[@mousedorff453]

Hi Professor Osborne, I was wondering if you've seen/heard of Peter Woit's book entitled "Quantum Theory, Groups and Representations"? That seems to discuss Quantum Theory with a focus on representation theory, along the lines of this lecture series you're providing. It might be worth checking out and I would also like to know your thoughts on it :D

[@tobiasjosborne]

many thanks for your comment: I have not read the book. I will take a look. (BTW: my course closely follows the excellent book of Serre, which you can regard as the textbook for this lecture series.)

[@tillerbrady6624]

Where can I learn about this more general stuff regarding symmetries in the context of physics such as that which you mention around 57:00 with fusion categories and replacing composition with categories and so forth?

[@tobiasjosborne]

it is by far not the best reference, but you could take a look at our notes arxiv.org/abs/1811.06670 . At least, these are a good place to find better references. I hope this helps; sincerely, Tobias Osborne

[@kevinullmann583]

Thank you for your videos! I would love to make a small donation as your lectures have provided so much value to me. Do you have a Patreon or some other platform where I could make a contribution to your work?

[@tobiasjosborne]

Many thanks for your comment! It is really humbling that you would be willing to make a donation! As it happens these videos are produced on (and with) university property. Because my work is publicly funded, I am actually not allowed to accept any form of payment or donation. My channel is not monetised. However, I am currently in the process of finding a legal way to donate potential profits to charity (not so easy, but I am investigating possibilities). If I manage to find a good way to do this then I will revisit this comment and post about ways to contribute. Until then, best wishes!

[@cantcommute]

do these lectures have problem sheets included? i would like to follow along whilst doing the problems

[@tobiasjosborne]

Thankyou for your comment. Problem sheets will not be distributed for this course. (As a substitute you can just do the problems in the book of Serre as they are well designed.)

[@cantcommute]

@@tobiasjosborne ok, thank you!

[@xuhuicheng909]

Wonderful course！And would you like to share your lecture notes online？

[@tobiasjosborne]

I don't really have notes; I work mostly from the book I recommended and add stuff as I go. But I believe someone is typing them up.

[@connorbrown5267]

The board cleaning is never not satisfying to watch

[@mockingbirdsphysicschannel9774]

I am typesetting the notes for these lectures. Anyone would like to collaborate?

[@apoorvpotnis]

Hey, have you typeset the notes? I am interested in contributing if all the notes are not completely typeset yet.