Introduction to Groups, Invariants and Particles

Group Theory, with its emphasis on Lie Groups and their application to the study of symmetries of the fundamental constituents of matter is introduced at a level suitable for Seniors and advanced Juniors majoring in the Physical Sciences. The book has its origin in a one-semester course that Professor Firk taught at Yale University for more than ten years. It is not generally appreciated by Physicists that continuous transformation groups (Lie Groups) originated in the Theory of Differential Equations. The infinitesimal generators of Lie Groups therefore have forms that involve differential operators and their commutators, and these operators and their algebraic properties have found, and continue to find, a natural place in the development of Quantum Physics. Topics covered include: Galois Groups Algebraic Invariants Invariants of Physics Groups − Concrete and Abstract Lie’s Differential Equation Lie’s Continuous Transformation Groups Matrix Representations of Groups Lie Groups of Transformations Group Structure of Lorentz Transformations Groups and the Structure of Matter Lie Groups and the Conservation Laws of the Physical Universe