Best / suggested / great Classical Field Theory texts?

[jjustinn]

Hey everyone,

I'm looking for some books that really dig into the topic of classical field theory -- and not necessarily just the fields that were known during the heyday of classical physics (electromagnetic / gravitational), but not necessarily all about Yang-Mills and Dirac fields, either.

It's sort of difficult to describe exactly what I'm looking for (which is probably why I'm having trouble finding a book that fits the bill), so maybe the best thing to do would be to list books that I do have, and how closely they fit:

Burgess - Classical Covariant Fields. This is the benchmark. Basically, I'm looking for something that covers the same type of topics that this one does, but perhaps going in-depth on fewer topics.

DeWitt - Dynamical Theory of Groups & Fields. The opening paragraph of this book lays out well exactly what I'm not looking for:

A chief goal of these lectures is to develop a framework within the quantization of fields ... may be carried out. ...[T]he goal of quantization means that we shall stress the quantum outlook from the beginning, even in preliminary investigations at the classical level.

This seems to be a common thread in virtually every book on field theory -- even many of those that are nominally supposed to be about classical field theory in particular.

Binz / Sniatycki / Fischer - Geometry of Classical Fields. Reading the TOC of this on Amazon, I thought WOW, this sounds great. But when I picked it up, not only did I find the unformatted text almost unreadable, but there is almost NO reference to physical applications.
Also, this seems like it's more an advanced differential geometry text than a field theory text, though if the topics were tied back to physical applications, that would probably pass muster.

Soper - Classical Field Theory. I like this one, but it's pretty basic. It was a great primer, but I'm looking for something slightly more advanced (or perhaps at about the same level of 'difficulty' of the non-introductory chapters, but with a broader range of topics).

Barut - Electrodynamics and Classical Theory of Fields and Particles. I'd compare this one to Soper. Really good text, well-written and original, grounded in reality -- but very focused on electrodynamics..which makes sense given the title, but again, I'm looking for maybe this depth on more / different topics.

Doughty - Lagrangian Interaction, Felsager - Geometry, Particles and Fields. Just bought these two. From the TOC, they seem like they touch on classical field theory, but only as a stepping stone to QFT.

Ng - Introduction to Classical and Quantum Fields. Given that classical fields were in the title, I was a little disappointed at how little a role they played.

Lifgarbagez / Landau - The Classical Theory of Fields. I'm probably not going to make any friends saying this, but I just can't get into the Landau books. They just feel...dated. I was again disappointed by the fact that although it was called "classical theory of fields", which I took to be "fields in general", it was focused on pretty basic electrodynamics / gravity.

...is that enough to go on? Or have I just confused and alienated everyone?

Any suggestions would be great.

Thanks,
Justin

 

[TonyG]

Dear Justin,

Thank you for posting on this forum and sharing your interest in classical field theory. I can understand your frustration in finding a book that covers the specific topics you are looking for. Classical field theory is a broad subject and it can be difficult to find a book that covers all the topics you are interested in without delving into quantum field theory.

Based on the books you have listed and your criteria, I would recommend the following books:

1. "Classical Field Theory" by Francis E. Low - This book covers a wide range of topics in classical field theory, including electromagnetic and gravitational fields, as well as Yang-Mills and Dirac fields. It also goes into depth on fewer topics, which seems to be what you are looking for.

2. "Classical Field Theory" by Davison E. Soper - This book is similar to the one you mentioned by the same author, but it covers more advanced topics. It also includes a section on classical electrodynamics, which may be of interest to you.

3. "Classical Field Theory: On Electrodynamics, Non-Abelian Gauge Theories and Gravitation" by Florian Scheck - This book covers classical field theory from a modern perspective, including discussions on electrodynamics, non-Abelian gauge theories, and gravitation. It also has a section on the geometrical foundations of classical field theory.

4. "Classical Field Theory" by Gleb Arutyunov and Serge Kuzenko - This book covers a wide range of topics in classical field theory, including classical electrodynamics, Yang-Mills theory, and gravity. It also has a section on the geometrical foundations of classical field theory.

I hope these suggestions are helpful in your search for a book on classical field theory. I also recommend checking out reviews and sample chapters of these books to see if they meet your criteria. Good luck in your studies!