Summary

I picked up a copy of Nadir Jeevnajee’s An Introduction to Tensors and Group Theory for Physicists a few months ago with the intent of skimming through and spending most of my time in reference texts. To my pleasant surprise, I found this text to be self contained - requiring little to no references. The presentation is at once mathematically rigorous and physically intuitive, alluding to well-known examples from physics throughout. I’ve found this text to be such a great introduction to tensors that I have even recommended it to computer-scientist colleagues of mine who have no interest in physics. I whole-heartedly recommend it to anyone interesting in becoming more familiar with tensors and elementary group / representation theory.

Part I: Tensors

The presentation of tensors as multilinear functions achieves a remarkable degree of exposition, and arrives at all the more heuristic definitions of tensors as derived from the simple multilinear-map definitions. This gave the impression of a more solid ground basis for many subsequent tensorial notations and usages.

The derivation of commonly assumed definitions is most satisfying. Specifically, the definitions of the adjoint operator and tensor product are much simpler than the more commonly given “behavioral” definitions presented in physics. I appreciated the rigorous yet succinct treatment of the tensor and wedge products.

Part II: Group Theory

Though I am still working through the last part of chapter 6, I must admit I found this section to be superbly clear. The methodical, sequential development of topics in Lie theory were especially thoughtful. The presentation of Lie algebra elements as derivatives of Lie group elements yielded the conventional tangent-space definitions nicely.

At the same time, Jeevanjee also presents many common groups and the important relations between them, such as the double-cover relationship of SU(2) and SO(3). He also presents the higher-level relations between the various common groups, such as the quantum implications of the Lorentz (improper) group. Good stuff!

Solutions

As I read through the text I’m compiling some solutions. Much to my fortunate suprise, Dr. Jeevanjee has welcomed these solutions as contributions to his solutions manual which he has published on Overleaf here: Solutions Manual.