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Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

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Page 1: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron
Page 2: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

Part B: Quantum Electrodynamics (QED)

Page 3: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 2. Effective approach to QED: Green's function method

Page 4: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 2. Effective approach to QED: Green's function method

Page 5: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 2. Effective approach to QED: Green's function method

Page 6: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 2. Effective approach to QED: Green's function method

Page 7: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 2. Effective approach to QED: Green's function method

Page 8: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 2. Effective approach to QED: Green's function method

Page 9: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 2. Effective approach to QED: Green's function method

Page 10: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 2. Effective approach to QED: Green's function method - 2

Page 11: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 2. Effective approach to QED: Green's function method - 2

Page 12: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 2. Effective approach to QED: Green's function method - 2

Page 13: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 2. Effective approach to QED: Green's function method - 2

Page 14: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 2. Effective approach to QED: Green's function method - 2

Page 15: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 2. Effective approach to QED: Green's function method - 2

Page 16: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 2. Effective approach to QED: Green's function method - 3

Page 17: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 2. Effective approach to QED: Green's function method - 3

Page 18: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 2. Effective approach to QED: Green's function method - 3

Page 19: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 2. Effective approach to QED: Green's function method - 3

2

Page 20: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 4. Feynman diagrams of QED – Feynman rules

External lines:

Page 21: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 4. Feynman diagrams of QED

Internal lines:

Page 22: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 4. Feynman diagrams of QED

Page 23: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 4. Feynman diagrams of QED

Example: Elastic electron-muon scattering:

Page 24: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

Transition probability:

B – 4. Feynman diagrams of QED

Page 25: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 5. Introduction to regularization and renormalization of QED

Infinities in loops:

Page 26: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 5. Introduction to regularization and renormalization of QED

Infinities in loops:

Page 27: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 5. Introduction to regularization and renormalization of QED

Dressed fermionic propagator:

Page 28: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 5. Introduction to regularization and renormalization of QED

Higher order corrections:

Page 29: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 5. Introduction to regularization and renormalization of QED

Pauli-Villars regularization:

Page 30: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 5. Introduction to regularization and renormalization of QED

Regularization schemes:

Page 31: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 5. Introduction to regularization and renormalization of QED

Electron mass renormalization:

Page 32: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 5. Introduction to regularization and renormalization of QED

Electron mass renormalization:

Page 33: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 5. Introduction to regularization and renormalization of QED

Electron self-energy loop renormalization:

Page 34: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 5. Introduction to regularization and renormalization of QED

Electron self-energy loop renormalization:

Page 35: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 5. Introduction to regularization and renormalization of QED

Fermionic loop - regularization:

Page 36: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 5. Introduction to regularization and renormalization of QED

Charge renormalization:

Page 37: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 5. Introduction to regularization and renormalization of QED

Charge renormalization:

Page 38: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 5. Introduction to regularization and renormalization of QED

Vertex corrections:

Page 39: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 5. Introduction to regularization and renormalization of QED

Vertex corrections:

Page 40: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 5. Introduction to regularization and renormalization of QED

Lamb shift:

Page 41: Part B: Quantum Electrodynamics (QED) - ift.uni.wroc.plblaschke/vorles/QED_Exam_Guideline_2016-17.pdf · B – 5. Introduction to regularization and renormalization of QED Electron

B – 5. Introduction to regularization and renormalization of QED

Lamb shift: