Compton Scattering Sum Rules for Massive Vector Bosons

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Contents 3.4 Optical Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.5 Derivation of Forward Dispersion Relations . . . . . . . . . . . . . . . . 35 4 Testing the Sum Rules in QFT 39 4.1 QFT: Yang-Mills Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.1.2 Yang-Mills Theory . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.1.3 Derivation of the Yang-Mills Lagrangian . . . . . . . . . . . . . 42 4.1.4 Vertex for W − W Interaction . . . . . . . . . . . . . . . . . . . 43 4.2 Gauge Invariance: Ward-Takahashi Identities . . . . . . . . . . . . . . . 44 4.3 Tree-Level Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5 Quantum One-Loop Corrections: Symmetry of the Theory 49 5.1 Derivative GDH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.2 Gauge Invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.3 Vertex Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.4 Yang-Mills Tadpole Contribution . . . . . . . . . . . . . . . . . . . . . 57 5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 6 Conclusion and Outlook 63 A Feynman Rules 65 A.1 Feynman Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 A.2 Plane Wave Expansions . . . . . . . . . . . . . . . . . . . . . . . . . . 67 A.2.1 Massive Spin-1 Particles . . . . . . . . . . . . . . . . . . . . . . 67 A.2.2 Photon Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 B Loop Integration 71 B.1 Tensor Loop Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 B.2 Feynman-Schwinger Parametrization . . . . . . . . . . . . . . . . . . . 74 C Diagrams 75 C.1 Tree-level Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 C.2 Vertex Correction Diagrams . . . . . . . . . . . . . . . . . . . . . . . . 75 C.3 Momentum Shifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Bibliography 79 iv
Contents Acknowledgements 85 v
Page 1 and 2: Compton Scattering Sum Rules for Ma
Page 3: Contents Introduction vii 1 Physica
Page 8 and 9: Introduction Purpose of this Study
Page 10 and 11: Introduction Euclidian metric and s
Page 12 and 13: Chapter 1 Physical method the term
Page 14 and 15: Chapter 1 Physical method where the
Page 16 and 17: Chapter 1 Physical method Lagrangia
Page 18 and 19: Chapter 1 Physical method where F (
Page 20 and 21: Chapter 1 Physical method F (ν) (n
Page 22 and 23: Chapter 2 Lagrangian Description of
Page 34 and 35: Chapter 3 Compton Scattering and Su
Page 50 and 51: Chapter 4 Testing the Sum Rules in
Page 52 and 53: Chapter 4 Testing the Sum Rules in
Page 54 and 55:
Chapter 4 Testing the Sum Rules in
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Chapter 5 Quantum One-Loop Correcti
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 73 and 74:
Chapter 6 Conclusion and Outlook We
Page 75 and 76:
Appendix A Feynman Rules A.1 Feynma
Page 77 and 78:
A.2 Plane Wave Expansions A.2 Plane
Page 79:
A.2 Plane Wave Expansions Contracti
Page 82 and 83:
Appendix B Loop Integration Im l 0
Page 84 and 85:
Appendix B Loop Integration It is u
Page 86 and 87:
Appendix C Diagrams µ q β p k k
Page 89 and 90:
Bibliography [A + 06] J. Alcaraz et
Page 91 and 92:
Bibliography [DHK + 04] [DKT01] [DP
Page 93 and 94:
Bibliography [Nus72] [Pai67] [Pai68
Page 95:
Acknowledgements First and foremost
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Compton Scattering Sum Rules for Massive Vector Bosons

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