文档介绍：QUANTUM FIELD THEORY
Professor John W. Norbury
Physics Department
University of Wisconsin-Milwaukee
. Box 413
Milwaukee, WI 53201
November 20, 2000
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Contents
1 Lagrangian Field Theory 7
Units ................................ 7
Natural Units ....................... 7
Geometrical Units .................... 10
Covariant and Contravariant vectors .............. 11
Classical point particle mechanics ................ 12
Euler-Lagrange equation ................. 12
Hamilton’s equations ................... 14
Classical Field Theory ...................... 15
Noether’s Theorem ........................ 18
Spacetime Symmetries ...................... 24
Invariance under Translation .............. 24
Angular Momentum and Lorentz Transformations . . 25
Internal Symmetries ....................... 26
Summary ............................. 29
Covariant and contravariant vectors .......... 29
Classical point particle mechanics ............ 29
Classical
eld theory ................... 29
Noether’s theorem .................... 30
References and Notes ....................... 32
2 Symmetries & Group theory 33
Elements of Group Theory .................... 33
SO(2) ............................... 33
Transformation Properties of Fields .......... 34
Representations of SO(2) and U(1) ............... 35
Representations of SO(3) and SU(1) .............. 35
Representations of SO(N) .................... 36
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4 CONTENTS
3 Free Klein-Gordon Field 37
Klein-Gordon Equation ..................... 37
Probability and Current ..................... 39
Schrodinger equation ................... 39
Klein-Gordon Equation ................. 40
Classical Field Theory ...................... 41
Fourier Expansion & Momentum Space ............ 42
Klein-Gordon QFT ..................