Irreducible representations (irreps) for physicists. Introduction
Often, by using only the symmetry of a problem, it is possible to deduce a lot about its solution without performing any calculations more complicated than basic arithmetic. Here, we explain exactly how this is done, with each method illustrated by practical examples. This is the first video of a mini-course. Here, we introduce the definitions of representations and irreducible representations. The following videos will be uploaded later. If you're waiting for part 2, write in comments. Probably, after this I will find some time and motivation :) References: Heine, V. Group Theory in Quantum Mechanics. 1963. Dresselhaus, M. S., Dresselhaus, G., & Jorio, A. (2008). Group Theory. Springer-Verlag. doi: 10.1007/978-3-540-32899-5 E.L. Ivchenko, G.E. Pikus, "Superlattices and Other Heterostructures. Symmetry and Optical phenomena” http://www.ioffe.ru/coherent/index.ht... Useful links: • http://www.ioffe.ru/coherent/index.ht... Irreps tables: • http://symmetry.jacobs-university.de/ • http://www.gernot-katzers-spice-pages... • http://newton.ex.ac.uk/research/qsyst... • https://www.theochem.ru.nl/files/loca... • https://www.snokelab.com/symmetry-tables 00:00 Introduction, About the Course 00:28 Transformation of Functions under Rotations 03:46 Definition of a Group, Symmetry Group of the Triangle 05:10 Transformation of Functions in the Group C3v 09:36 Transformation of Functions in the Group C3v --- conclusion 12:03 Multiplication Table, Representations 13:37 Permutation Representation 14:18 Irreducible Representations 16:23 Formal Definitions
A Practical guide to representation theory
Irreducible representations (irreps) | Representation theory episode 3
F-Math -Ali Rastegar - Logic in the reverse direction
Representation theory: Introduction
Quantum Chemistry 12.13 - Determining Irreps
What is Lie theory? Here is the big picture. | Lie groups, algebras, brackets #3
What Are Electric and Magnetic Fields, Really? | Maxwell’s Equations: Part 1
do you know about the "reciprocal gamma function"??
But what is a Laplace Transform?
Representations of Finite Groups | Definitions and simple examples.
Group theory, abstraction, and the 196,883-dimensional monster
Symmetries and quantum mechanics: basics, Wigner's theorem, linear representations of groups
Group Theory and Particle Physics (feat. Rebecca Nelson)
When Math Isn’t Based in Reality
The FULL VIDEO of Trump they didn’t want released
Group Theory and Chemistry Basics 4: Character Tables and Representations
What is a Hilbert Space?
The Anti Trampoline Effect
