In physics language:

There is a moment in the study of theoretical physics where the student realizes that the universe does not speak in numbers, but in symmetries. It is a shift in perspective as profound as the Copernican revolution: the equations of nature are not merely describing what happens, but what is allowed to happen based on the invariance of laws.

Applies the previous theory to physical systems, specifically molecular symmetry and homogeneous vector bundles. Chapter 4: Compact Groups and Lie Groups

: Much of the book focuses on the group

While symplectic geometry is the language of classical Hamiltonian mechanics, Sternberg has long argued that it is equally foundational for , via deformation quantization.