GAUGE-FIELD THEORIES

Ulrich Mosel Institut f"ur Theoretische Physik, Universit"at Giessen

D-35392 Giessen, Germany

Vorlesung im Sommersemester 1996 an der JLU Giessen

September 10, 1996

Contents I Preliminaries 5 1 UNITS AND METRIC 7

1.1 Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Metric and Notation . . . . . . . . . . . . . . . . . . . . . . . 8

II Fundamentals of Field Theory 11 2 CLASSICAL FIELDS 13

2.1 Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . 13

2.1.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.1.1 Electrodynamics . . . . . . . . . . . . . . . . 15 2.1.1.2 Massive vector fields . . . . . . . . . . . . . . 17 2.1.1.3 Klein-Gordon fields . . . . . . . . . . . . . . 17 2.1.1.4 Dirac Fields . . . . . . . . . . . . . . . . . . 18 2.2 Symmetries and Conservation Laws . . . . . . . . . . . . . . . 19

2.2.1 Geometrical Space-Time Symmetries . . . . . . . . . . 19 2.2.2 Internal Symmetries . . . . . . . . . . . . . . . . . . . 21

III Global Symmetries 25 3 SYMMETRIES OF MESON AND BARYON SYSTEMS 27

3.1 U (1) Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.1.1 Properties of the Group U (1) . . . . . . . . . . . . . . 28 3.1.2 Structure of the Nucleon Lagrangian . . . . . . . . . . 30 3.2 SU (2) Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.2.1 Properties of the Group SU (2) . . . . . . . . . . . . . 32 3.2.2 Application to the Pion-Nucleon System . . . . . . . . 37

3.2.2.1 Symmetry of the Nucleon Lagrangian . . . . 37

1

2 CONTENTS