Representation theory of Lie groups and Lie algebras - Lec 17 - Frederic Schuller

[@nikitakazankov4099]

Great lecture, Dr. Schuller. I'm self-studying about QFT and Gauge Theories from an undergraduate math background and I find your lectures accessible, clear, useful and on point. Thanks.

[@jelmar35]

How did your studies turn out?

[@Maths_3.1415]

​@@jelmar35 you are too late to ask this bro

[@rutgermoody7204]

Absolutely the best lecture of its kind! I've always had trouble grasping this subject. This series of lectures builds it all up from logic to set theory to topology and then manifolds etc. Without going into so much detail that you loose track of the main story. This makes it all completely logical.

[@nicoskekchidis5869]

Hats off to you Dr. Schuller! I am enthusiast with computer science background who is immensely enjoying seemingly unapproachable Geometrical Anatomy of Theoretical Physics artfully presented by you. Scaffolding and building comprehension capacity approach taken in this monumental 25+ chapters course is very logical, intuitive and simply amazing. One Big Thank you!

[@danielpfeffer2473]

Beautifully concise presentation of Lie group representations at 1:17:30. Thank you, Professor.

[@GunsExplosivesnStuff]

39:26 ad is not faithful unless Z(L) = 0, and not irreducible unless L is simple.

[@esoegipson3010]

I so much enjoy, and understand every single step you take sir. You teach with much pedagogic and content skills. It is inert sir and i much confess that with you lectures, i make wonderful grades in mathematics undergraduate. Thanks sir

[@aboubacarnibirantiza4748]

Thank you for your series of lectures about the Lie theory. In your lectures, i learned a lot of things in geometric anatomy of theoreticla Physics.

[@kapoioBCS]

There is no -1/2 in the Casimir also, you just define the ξ's with the -1/2 that is missing i.e. ξ_i=-1/2 J_i

I think that the adjoint representation is faithful only when the center of the Lie Algebra is trivial.

[@AbrahamLozadaabe]

The problem sheet, 39:00 , has a "trick" (just kidding)

[@millerfour2071]

6:43, 13:27, 43:20, 47:59, 53:47, 1:00:30, 1:04:39, 1:10:34, 1:14:30 (c is 3/2, where xi is 2J, then J^2=c/2=3/4), 1:28:48, 1:30:20

[@synaestheziac]

What is this a list of?

[@andreshombriamate745]

The X*(i) of the associated basis are X*(i)=2X(i) to be ortonormal with the X(i) (in the case of the representation which uses Pauli matrices). So , the result is finally 3/4.

[@Zahrakharaghani]

thank you

[@lucagagliano5118]

I don't understand the point of SL(2,C) as example, isn't it defined as a set of matrices anyway? What's the point of the representation proposed?

[@varunmenon830]

The point is to understand the group structure of SL(2,C) in terms of its group actions on an arbitrary complex vector space. The key here is to represent the group actions of SL(2,C) as linear transformations (and not the elements themselves).

[@chasebender7473]

The group SL(2,C) is a group of matrices, but i believe you are refering to the representation of the Lie algebra sl(2,C) which, as far as we know from these lectures is identified with the tangent space of the group SL(2,C).

[@joshuatindall4743]

20:18 “An eye for an i”

[@kapoioBCS]

The definition of Casimir operator should be on compact faithful Lie algebras L. Not on every Lie algebra.

[@blackflan]

on faithful representations of compact Lie algebras*

[@thephysicistcuber175]

On faithful representation of semisimple Lie algebras*.

[@StephenCrowley-dx1ej]

Holy s*** I was following along and then he just starts like shouting out binary code like 010110100001 completely incomprehensible it's like me going up in like shouting out assembler code to my expression compiler it's like just point and read anyway this video is like 8 years old I hope this dude is still doing good cuz his lectures are great

[@TheBanjoShowOfficial]

I literally understand zero of this why am I here

[@luisgeniole369]

uuuhhh representation

[@frankdimeglio8216]

ON THE ABSOLUTE PHYSICAL EQUIVALENCY AND BALANCING OF E=MC2 AND F=MA: It is a very great truth in physics that the ability of thought to DESCRIBE OR reconfigure sensory experience is ULTIMATELY dependent upon the extent to which THOUGHT IS SIMILAR TO sensory experience, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. (THOUGHTS ARE INVISIBLE.) INDEED, E=mc2 IS DIRECTLY and fundamentally derived from F=ma; AS time dilation proves that electromagnetism/ENERGY IS GRAVITY. Therefore, ultimately and truly, time is possible/potential AND actual IN BALANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. In fact, INSTANTANEITY is FUNDAMENTAL to the FULL and proper understanding of physics/physical experience; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. THE stars AND PLANETS are POINTS in the night sky. A PHOTON may be placed at the center of what is THE SUN (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the speed of light; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. E=mc2 IS F=ma. GREAT !!! BALANCE AND completeness go hand in hand. It all CLEARLY makes perfect sense. (Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black.) The INTEGRATED EXTENSIVENESS of THOUGHT (AND description) is improved in the truly superior mind. Gravity IS ELECTROMAGNETISM/ENERGY. By Frank DiMeglio

[@tzimmermann]

This is not a lecture on quantum woo. Good god...

[@smalljbug]

It's super entertaining that on so many lectures about ACTUAL math, there's some crackpot pseudo-science in the comments, enlightening us all. Digging the capitals also.