Video/Noether's Theorem Explained (Part 1/6) - Introduction

Miller, Noah (Jan 9, 2019). Noether's Theorem Explained (Part 1/6) - Introduction. local page: NoahExplainsPhysics. 

Symmetries can be studied by groups and actions (or operators) applied to it. The foundational ideas of symmetries came from Emmy Noether and here paper:Invariant Variation Problems. Note that these three terms are represented in plural form. The ability to count the number of symmetries or explicitly distinguish the consequences of actions in sequences and in combinations are the core concepts of symmetry studies. Symmetry is one critical property of being Equivalent, and is directly linked with Adjoint Functors, a.k.a. Galois Connections. Brendan Fong also discuss the notion of symmetry in his doctoral thesis.

Connection with Least Action and Lagrange Mechanics

It would be helpful to learn more about the Principle of Least Actionand Lagrangian Mechanics after learning the notion of symmetry.

For people who are interested in Symmetry, please watch the video by Group Theory by Gareth Jones on Serious Science. Another reference is the youtuber, Number Cruncher

Video Series

There is a series of videos:

1. Introduction
2. Momentum and Spatial Translations
3. Angular Momentum and Rotations
4. Proof
5. Total Derivatives
6. Energy and Time Translations

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