Symmetries, Conservation Laws and Variational Principles - Part II

Explore the second part of a comprehensive lecture on symmetries, conservation laws, and variational principles delivered by Prof. Ian Anderson from Utah State University. Delve into the mathematics surrounding the renowned Noether Theorems in the calculus of variations. Examine various types of symmetries, including external, internal, and generalized symmetries, with practical examples and symbolic representations. Investigate conservation laws, from first integrals of ODEs to classical conservation laws and their applications in general relativity. Gain insights into the Noether Theorems, their variations, and practical examples. Analyze the Taken's Problem, an inverse Noether Theorem, and explore its implications. Conclude with a study of invariant variational problems and differential invariants. This lecture is part of the SCREAM project, focusing on Cartan and parabolic geometries and their interactions with mechanical systems, integrable systems, and cosmology.

I. Anderson (Utah State University): Symmetries, Conservation Laws and Variational Principles, p. II