Noether's Theorem, Symmetries & Lorentz/Poincare Group Self-Study - help?

[ZenMaster]

Hello folks,

I'm interested in getting a much deeper understanding of symmetries and how they pretty much define the universe; e.g. translation symmetry in time = Conservation of Energy?? according to Wikipedia. I'm *extremely* interested in how symmetries lead to universal laws.

My level of education is up to 3.5 years of Mathematics/Statistics in university.. I had to drop due to funding issues. I wasn't a spectacular student but I would have graduated. I learned some set theory, but by now my memories foggy.

Can anyone recommend resources to study from? Online preferred for convenience, but I'm definitely willing to shell out for decent textbooks (preferred university level, since casual "Chapters-ish" books gloss over the real explanations).

Thanks for any suggestions you may have! I'll take any and every one.

Dan

 

[eljose79]

Hello Dan,

It's great to see your interest in symmetries and their role in defining the universe. I can definitely attest to the fact that symmetries play a crucial role in understanding the fundamental laws of nature.

To start off, I would recommend looking into the concept of Noether's theorem, which is a fundamental principle that connects symmetries to conservation laws. This theorem states that for every continuous symmetry in a physical system, there exists a corresponding conserved quantity. This means that the laws of nature are essentially a result of symmetries in the universe.

In terms of resources, I would highly recommend the book "Symmetry and the Standard Model: Mathematics and Particle Physics" by Matthew Robinson. It provides a comprehensive overview of the role of symmetries in particle physics and their connection to the standard model. Another great resource is the online course "Symmetry, Structure, and Tensor Properties of Materials" offered by MIT OpenCourseWare.

If you're looking for a more mathematical approach, I would suggest "Symmetry and the Beautiful Universe" by Leon M. Lederman and Christopher T. Hill. This book delves into the mathematical concepts behind symmetries and their applications in physics.

I hope these suggestions help you in your pursuit of understanding symmetries and their significance in the universe. Best of luck in your studies!