文档介绍：Introduction
to
Groups, Invariants
and
Particles
Frank W. K. Firk, Professor Emeritus of Physics, Yale University
2000
ii
iii
CONTENTS
Preface v
1. Introduction 1
2. Galois Groups 4
3. Some Algebraic Invariants 15
4. Some Invariants of Physics 23
5. Groups - Concrete and Abstract 37
6. Lie’s Differential Equation, Infinitesimal Rotations,
and Angular Momentum Operators 50
7. Lie’s Continuous Transformation Groups 61
8. Properties of n-Variable, r-Parameter Lie Groups 71
9. Matrix Representations of Groups 76
10. Some Lie Groups of Transformations 87
11. The Group Structure of Lorentz Transformations 100
12. Isospin 107
13. Groups and the Structure of Matter 120
14. Lie Groups and the Conservation Laws of the Physical Universe 150
15. Bibliography 155
iv
v
PRE FACE
This int roduc tion to Gro up The ory, wit h its emp hasis on Lie Gro ups
and the ir app licat ion to the stu dy of sym metri es of the fun damen tal
con stituents of mat ter, has its ori gin in a one -semester cou rse tha t I tau ght
at Yal e Uni versity for mor e tha n ten yea rs. The cou rse was dev eloped for
Sen iors, and adv anced Jun iors, maj oring in the Phy sical Sci ences. The
stu dents had gen erall pleted the cor e cou rses for the ir maj ors, and
had tak en int ermed iate level cou rses in Lin ear Alg ebra, Rea l plex
Ana lysis , Ord inary Lin ear Dif feren tial Equ ation s, and som e of the Spe cial
Fun ction s of Phy sics. Gro up The ory was not a mat hemat ical req uirem ent
for a deg ree in the Phy sical Sci ences. The maj ority of existing
und ergra duate tex tbook s on Gro up The ory and its app licat ions in Phy sics
ten d to be eit her hig hly qua litat ive or hig hly mat hematical. The pur pose of
thi s int roduc tion is to ste er a mid dle cou rse tha t pro vides the stu dent wit h
a sou nd mat hemat ical bas is for stu dying the sym metry pro perti es of the
fun damen tal par ticle s. It is not gen erall y app reciated by