Lecture Notes on Mathematical Methods of Classical Physics

TL;DR

This comprehensive lecture notes collection covers advanced mathematical methods used in classical physics, including Lagrangian and Hamiltonian mechanics, Hamilton-Jacobi theory, and classical field theories like gauge theory and general relativity.

Contribution

It provides a mathematically rigorous and unified presentation of classical physics topics, integrating modern geometric approaches and field theory examples for graduate students and researchers.

Findings

Detailed exposition of Lagrangian and Hamiltonian formalisms

Introduction to jet bundle formulation of field theories

Application of geometric methods to classical field theories

Abstract

These notes grew out of a lecture course on mathematical methods of classical physics for students of mathematics and mathematical physics at the master's level. Also, physicists with a strong interest in mathematics may find this text useful as a resource complementary to existing textbooks on classical physics. Topics include Lagrangian Mechanics, Hamiltonian Mechanics, Hamilton-Jacobi Theory, as well as Classical Field Theory formulated in the language of jet bundles. The latter topic also covers important examples of field theories such as sigma models, gauge theory, and Einstein's theory of general relativity.