Classical to Quantum | Quantization and Lie group Representation Theory | Wild Egg Maths

This is an overview video where I briefly sketch one of the general aims and direction of this series (Classical to Quantum for Members of the Channel) to investigate mathematical aspects of quantum mechanics (QM), special relativity (SR) and related aspects of the standard model (SM).

In particular I want to delve into the role of representation theory of Lie groups in modern physics, and the remarkable parallels between the rise of QM in the 1930's and developments in harmonic analysis on Lie groups around the same time, leading to a curious role for notions of quantization which was clarified in the 1960's by Kirillov and became the topic called "geometric quantization", pushed along also by Kostant and Souriau and others.

This theory features the symplectic geometry of coadjoint orbits of Lie groups, which play the role of classical mechanical systems, with the associated representations playing the role of their quantum analogs. So the purely abstract theory of representations of Lie groups, such as S^1, SU(2) and SU(3) which figure prominently in the SM, forms a natural laboratory to investigate the wider meaning and significance of QM, and perhaps sheds some light on which interpretations of that subject are likely to be the most fruitful.

Video Contents:

0:01 Introduction: Integration on Circles and Physics
4:00 Quantization: Connecting Classical and Quantum Mechanics
8:14 Harmonic Analysis and Peter-Weyl Theorem
10:25 Coadjoint Orbits and Classical Mechanical Systems
14:51 Invitation to Join the Mathematical-Physical Exploration

My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/...

My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.

Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/...

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