# Introduction to Groups, Invariants & Particles

###
About *Introduction to Groups, Invariants & Particles:*

Excerpts from book and site:

Introduction to Groups, Invariants & Particles is a book for Seniors and advanced Juniors who are majoring in the Physical Sciences or Mathematics. The book places the subject matter in its historical context with discussions of Galois groups, algebraic invariants, Lie groups and differential equations, presented at a level that is not the standard fare for students majoring in the Physical Sciences. A sound mathematical basis is thereby provided for the study of special unitary groups and their applications to Particle Physics.

This introduction to Group The ory, with its emphasis on Lie Groups and their application to the study of symmetries of the fundamental constituents of matter, has its origin in a one-semester course that I taught at Yale University for more than ten years. The course was developed for Seniors, and advanced Juniors, majoring in the Physical Sciences . The students had generally completed the core courses for their majors, and had taken intermediate level courses in Linear Algebra, Real and Complex Analysis , Ordinary Linear Differential Equations, and some of the Special Functions of Physics. Group Theory was not a mathematical requirement for a degree in the Physical Sciences . The majority of existing undergraduate textbooks on Group Theory and its applications in Physics tend to be either highly qualitative or highly mathematical. The purpose of this introduction is to steer a middle course that provides the student with a sound mathematical basis for studying the symmetry properties of the

fundamental particles. 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.

Introduction to Groups, Invariants & Particles is a book for Seniors and advanced Juniors who are majoring in the Physical Sciences or Mathematics. The book places the subject matter in its historical context with discussions of Galois groups, algebraic invariants, Lie groups and differential equations, presented at a level that is not the standard fare for students majoring in the Physical Sciences. A sound mathematical basis is thereby provided for the study of special unitary groups and their applications to Particle Physics.

This introduction to Group The ory, with its emphasis on Lie Groups and their application to the study of symmetries of the fundamental constituents of matter, has its origin in a one-semester course that I taught at Yale University for more than ten years. The course was developed for Seniors, and advanced Juniors, majoring in the Physical Sciences . The students had generally completed the core courses for their majors, and had taken intermediate level courses in Linear Algebra, Real and Complex Analysis , Ordinary Linear Differential Equations, and some of the Special Functions of Physics. Group Theory was not a mathematical requirement for a degree in the Physical Sciences . The majority of existing undergraduate textbooks on Group Theory and its applications in Physics tend to be either highly qualitative or highly mathematical. The purpose of this introduction is to steer a middle course that provides the student with a sound mathematical basis for studying the symmetry properties of the

fundamental particles. 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.