A Modern Approach to Mathematical Physics: From 40 Years ago

 One of the novel studies into mathematical and theoretical physics over the last decade has been the study of topological quantum field theories and so-called "higher form" symmetries.  

This area of study, though extremely important and flourishing, has been gate-kept to a smaller collection of researchers worldwide due to the level of mathematics (which is quite alien to most physicists) needed to even begin studying the topic. 

The main culprit of this strife has been the infamous study of category theory (the field of mathematics which generalises all mathematical structures), which has long been the poster boy and plaything for mathematicians for decades (and more recently computer scientists).  Many reviews on the subject (written by physicists no less), have been rather unwieldy. 

In this regard, Geroch has been some sort of prophet when it comes to predicting the need for this text (considering this text was first published in 1985).  

The text provides an excellent jumping-on point for novices in category theory, especially physicists. The text begins by outlining the basics of category theory before extending them to include all aspects of mathematical physics that a professional physicist could need; to list some: vector spaces, aspects of topology and operators. This text also has the added benefit of applying these ideas to physical examples familiar to most physicists (Minkowski and Fock space) to help solidify the ideas presented in the preceding chapters.

Another quirk of this historical text are the hand-drawn figures sprawled generously (to good effect) throughout. This figure helps improve the clarity and pedological nature of the text.  

Overall, I would recommend this text to any graduate (or above) theoretical physicist who is keen to develop into the great unknown of category theory within mathematical physics. 

Mathematical Physics (Chicago Lectures in Physics)

By Robert Geroch
ISBN: 978-0226288628
Publisher
University of Chicago Press




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