Quantum Field Theory I

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Preface These are lecture notes to QFT I, supplementing the course held in the winter term 2005. The course is just an introductory one, the whole scheme being QFT I basic concepts and formalism scalar fields, toy-models QFT II electrons and photons quantum electrodynamics Renormalization pitfalls of the perturbation theory treatment of infinities Introduction to the Standard Model quarks, leptons, intermediate bosons quantum chromodynamics, electroweak theory Initially, the aimofthistext wasnottocompete with the textbooksavailable on the market, but rather to provide a set of hopefully useful comments and remarks to some of the existing courses. We chose An Introduction to Quantum Field Theory by Peskin and Schroeder, since this seemed, and still seems, to be the standard modern textbook on the subject. Taking this book as a core, the original plan was • to reorganize the material in a bit different way • to offer sometimes a slightly different point of view • to add some material 1 Eventually, the text became more and more self-contained, and the resemblance to the Peskin-Schroeder became weaker and weaker. At the present point, the text has very little to do with the Peskin-Schroeder, except perhaps the largely common notation. 1 Almost everything we have added can be found in some well-known texts, the most important sources were perhaps The Quantum Theory of Fields by Weinberg, Diagrammar by t’Hooft and Veltman and some texts on nonrelativistic quantum mechanics of many-particle systems.
Page 1: Quantum Field Theory I Martin Mojž
Page 6 and 7: Chapter 1 Introductions Quantum fie
Page 8 and 9: 1.1. CONCLUSIONS 3 1.1.1 Feynman ru
Page 10 and 11: 1.1. CONCLUSIONS 5 propagators Prop
Page 12 and 13: 1.1. CONCLUSIONS 7 Now to the secon
Page 14 and 15: 1.1. CONCLUSIONS 9 the factor corre
Page 16 and 17: 1.1. CONCLUSIONS 11 1.1.3 Scatterin
Page 18 and 19: 1.1. CONCLUSIONS 13 rough estimatio
Page 20 and 21: 1.1. CONCLUSIONS 15 1.1.5 A redunda
Page 22 and 23: 1.2. MANY-BODY QUANTUM MECHANICS 17
Page 44 and 45: 1.3. RELATIVITY AND QUANTUM THEORY
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Chapter 2 Free Scalar Quantum Field
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2.1. ELEMENTS OF CLASSICAL FIELD TH
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2.2. CANONICAL QUANTIZATION 57 Exam
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2.2. CANONICAL QUANTIZATION 59 The
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2.2. CANONICAL QUANTIZATION 61 Fort
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2.2. CANONICAL QUANTIZATION 63 Now
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2.2. CANONICAL QUANTIZATION 65 Hilb
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2.2. CANONICAL QUANTIZATION 67 Quas
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2.2. CANONICAL QUANTIZATION 69 For
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2.2. CANONICAL QUANTIZATION 71 Anim
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Chapter 3 Interacting Quantum Field
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3.1. NAIVE APPROACH 75 3.1.1 Intera
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3.1. NAIVE APPROACH 77 perturbation
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3.1. NAIVE APPROACH 79 green functi
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3.1. NAIVE APPROACH 81 Wick’s the
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3.1. NAIVE APPROACH 83 Feynman rule
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3.1. NAIVE APPROACH 85 derivative c
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3.1. NAIVE APPROACH 87 propagator I
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3.1. NAIVE APPROACH 89 One may, of
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3.1. NAIVE APPROACH 91 connected di
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3.1. NAIVE APPROACH 93 3.1.3 Cross-
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3.1. NAIVE APPROACH 95 1 2E jV Thef
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3.1. NAIVE APPROACH 97 For two part
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3.2. STANDARD APPROACH 99 Since H0
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3.2. STANDARD APPROACH 101 Green fu
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3.2. STANDARD APPROACH 103 non-pert
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3.2. STANDARD APPROACH 105 Having p
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3.2. STANDARD APPROACH 107 3.2.3 th
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3.2. STANDARD APPROACH 109 Remark:
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3.2. STANDARD APPROACH 111 ∣ The
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3.2. STANDARD APPROACH 113 Remark:
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