Book Recommendations
Book Recommendations
I am nowhere near being a book expert or a critic, especially in such a vast area of theoretical physics. However, I wanted to share the books that I had a good time with and had time to reflect on. These are some books I had fun reading and recommend.
Mathematical Methods of Classical Mechanics: V. I. Arnold
This is one of my favorite books of all time! It elegantly defines classical mechanics using mathematical apparatus such as symplectic geometry, manifolds and Lie algebras. However, he does not abstract the theory by doing that. As a matter of fact, he strongly opposes abstracting and clearly shows the connections between physics and mathematics in a vivid way.
Classical Mechanics - Herbert Goldstein
Some may look for a more practical book to learn classical mechanics rather than delving into the mathematical foundations. Then, Goldstein's book should be just what you need.
Modern Quantum Mechanics - J. J. Sakurai
This was the first book that introduced me to the subject of Quantum Mechanics. It explains the basics in a concise and effective way. The problems were super useful and taught me a lot. I have not read the Approximations Methods and the following chapters yet. Apparantly, I need to read them as soon as possible.
Introductory Quantum Mechanics - Richard Liboff
I have read this book for my undergraduate Quantum Physics courses and I enjoyed it a lot.
Quantum Field Theory - Mark Srednicki
This was the first book that introduced me to Quantum Field Theory, and I found it to be brilliant, self-contained, and user-friendly. Clearly stated prerequisites to each chapter make the book easy to read. The calculations are carried out more explicitly than in any other QFT book that I am aware of. I only feel that it could have explained certain concepts more intuitively. However, this may just be due to my own limited background when I first read it as a sophomore. For instance, including a few applications to condensed matter physics would have been a great addition. Overall, this is a very effective book, and I definitely recommend reading it twice or concurrently with another QFT text.
Quantum Field Theory Lectures - Sidney Coleman
This is a huge book which I read only a small portion of it. Apart from beautiful conceptual discussions, the most important aspect of this book which I really like is its diverse and comprehensive problems.
Classical Theory of Gauge Fields - Valery Rubakov
I started to read this book to learn about topological solitons and instantons. Therefore, I was only able to read some sections of Part I, and Part II and they were brilliant. I hope I will have more time to read Part III where the results of interaction between fermions and topological gauge fields are discussed.
Differential Geometry for Physicists - Bo-Yu Hou and Bou-Yuan Hou
This is an excellent, though somewhat underrated, book for getting a good grasp of most of the mathematical language used in modern theoretical physics. I especially appreciate its completeness, lucid notation, and beautiful summary (formulae) tables. It begins with the basics of manifold theory and continues up to more advanced topics like the Atiyah-Singer index theorem and beyond. Hopefully, I will have more to enjoy this book.
Geometry, Topology and Physics - Mikio Nakahara
This is a renowned and more canonical text on this subject. I have not spent as much time on this book as I have on the first one, but I did thoroughly enjoy Chapter 9, where fiber bundles are discussed beautifully. Moreover, there are some very nice applications in condensed matter physics (Chapters 4.8 and 4.9) and string theory (Chapter 14), which are particularly useful.