Physics - Srednicki, M - Quantum Field Theory [Cambridge, 2007].pdf

Quantum Field Theory
Mark Srednicki
University of California, Santa Barbara
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c 2006 by M. Srednicki
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To my parents
Casimir and Helen Srednicki
with gratitude
Contents
Preface for Students 8
Preface for Instructors 12
Acknowledgments 16
I Spin Zero 18
1 Attempts at relativistic quantum mechanics 19
2 Lorentz Invariance (prerequisite: 1) 30
3 Canonical Quantization of Scalar Fields (2) 36
4 The Spin-Statistics Theorem (3) 45
5 The LSZ Reduction Formula (3) 49
6 Path Integrals in Quantum Mechanics 57
7 The Path Integral for the Harmonic Oscillator (6) 63
8 The Path Integral for Free Field Theory (3, 7) 67
9 The Path Integral for Interacting Field Theory (8) 71
10 Scattering Amplitudes and the Feynman Rules (5, 9) 87
11 Cross Sections and Decay Rates (10) 93
12 Dimensional Analysis with ¯h = c =1(3) 104
13 The Lehmann-K¨all´en Form of the Exact Propagator (9) 106
14 Loop Corrections to the Propagator (10, 12, 13) 109
15TheOne-LoopCorrectioninLehmann-K¨all´en Form (14) 120
16 Loop Corrections to the Vertex (14) 124
17 Other 1PI Vertices (16) 127
18 Higher-Order Corrections and Renormalizability (17) 129
4
19 Perturbation Theory to All Orders (18) 133
20 Two-Particle Elastic Scattering at One Loop (19) 135
21 The Quantum Action (19) 139
22 Continuous Symmetries and Conserved Currents (8) 144
23 Discrete Symmetries: P , T , C,andZ (22) 152
24 Nonabelian Symmetries (22) 157
25 Unstable Particles and Resonances (14) 161
26 Infrared Divergences (20) 167
27 Other Renormalization Schemes (26) 172
28 The Renormalization Group (27) 178
29 Effective Field Theory (28) 185
30 Spontaneous Symmetry Breaking (21) 196
31 Broken Symmetry and Loop Corrections (30) 200
32 Spontaneous Breaking of Continuous Symmetries (22, 30)205
II Spin One Half 210
33 Representations of the Lorentz Group (2) 211
34 Left- and Righ