A (very) Brief Introduction to Lie Groups and Lie Algebras in Physics

Abstract:

The goal of the talk is to provide a few common examples of how Lie groups and Lie algebras are used in physics. One of the most important ideas in physics is symmetry. Loosely speaking, symmetry refers to transformations that leave the laws of physics the same. This statement can be expressed more precisely with group theory, the mathematics of symmetry. Lie groups refer to groups with continuous parameters, i.e. continuous transformations, and Lie algebras are associated with generators that produce infinitesimal transformations. This is a big subject and I can only mention few examples (rotational, spacetime and internal symmetries) that will serve as a modest introduction to the subject. Most importantly, I would like to convey the importance of the role of symmetry in physics.

Union College Math Department Home Page Comments to: math@union.edu Created automatically on: Fri Jul 20 16:17:18 EDT 2018