Mathematics

# Calculus on Manifolds

This is a great book for those who are learning General Relativity but are unsatisfied with the often wrong mathematics when the author tries to be mathematically rigorous. (I have Spacetime and Geometry by Sean Carroll in mind.) There are however a few shortcomings with this book: a) errors here and there, b) lack of an official solution manual, and c) lack of explanations necessary for the physical intuition behind mathematical formalism.

Mathematics

# Lie Algebras in Particle Physics

Errata and Notes Chapters 1 1.4 Irreducible representations On equivalence Note that \( S \) in Eq. (1.10) is in general not unitary. Therefore two equivalent representations do not just differ by a trivial choice of basis as claimed in the book. All representations of finite groups are equivalent to unitary representations, and we can always find a basis for any representation to have a unitary matrix form, although the basis will not be orthonormal in general.