Introduction Theoretical Physics

In other notes, we have explored many topics in physics, from classical mechanics, electromagnetism, optics to quantum mechanics, general relativity, and string theory. We now turn to a self-contained introduction to all the theoretical physics you need to know to understand modern research papers in physics. This includes a review of the necessary mathematics, as well as the physical concepts and theories that underpin modern physics.

To understand the latest research in physics, we must have a solid understanding of classical mechanics. This is often a neglected topic in modern physics education, but in fact classical mechanics is the foundation of all physics. The mathematics of classical mechanics is immensely complicated, covering ideas such as fiber bundles, symplectic geometry, Lie groups, and much more. As such, we will include a dedicated section on the mathematical foundations needed for theoretical physics.

For this section we will follow Mathematical Physics: A Modern Introduction to Its Foundations by Sadri Hassani, which is an excellent book that covers all the necessary mathematics needed for theoretical physics.