This is where the book builds muscle. The representation theory of finite groups is developed in full generality: irreducible representations (irreps), characters, Schur’s lemmas, and the great orthogonality theorem. Sternberg then applies these to molecular vibrations in chemistry and to the classification of atomic terms in spectroscopy. He famously includes a thorough discussion of the symmetric group, laying the groundwork for the Young tableaux that will reappear in particle physics.
The canonical reference for the keyword usually refers to the 1994 Cambridge University Press edition. The book is structured into three distinct parts, each escalating in complexity.
In the realm of theoretical physics, few mathematical tools are as indispensable as group theory. It provides the formal language for symmetry, and symmetry is the bedrock upon which modern physical laws are built. For students and researchers diving into this intersection, Shlomo Sternberg’s Group Theory and Physics is often cited as a seminal text.
Despite being published decades ago, the mathematics of symmetry hasn't changed. Whether you are studying the Standard Model of particle physics or the latest developments in topological insulators, the fundamental representations of Lie algebras discussed by Sternberg remain the starting point.
Sternberg is a master of geometry. The text does not restrict itself to algebraic manipulation but visualizes groups as geometric objects. For instance, his treatment of $SO(3)$ and $SU(2)$ is not just a matrix exercise but a geometric exploration of rotations and spinors. This geometric intuition is crucial for students attempting to visualize higher-dimensional symmetries in particle physics.
