Concepts in Quantum Field Theory: A Practitioner's Toolkit

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Springer, Aug 28, 2015 - Science - 190 pages

This book uses less strict yet still formal mathematical language to clarify a variety of concepts in Quantum Field Theory that remain somewhat “fuzzy” in many books designed for undergraduates and fresh graduates. The aim is not to replace formal books on Quantum Field Theory, but rather to offer a helpful complementary tool for beginners in the field. Features include a reader-friendly introduction to tensor calculus and the concept of manifolds; a simple and robust treatment for dimensional regularization; a consistent explanation of the renormalization procedure, step by step and in a transparent manner at all orders, using the QED Lagrangian; and extensive treatment of infrared as well as ultraviolet divergences. The most general (Lorentz invariant) form of Noether's theorem is presented and applied to a few simple yet relevant examples in Quantum Field Theory. These and further interesting topics are addressed in a way that will be accessible for the target readership. Some familiarity with basic notions of Quantum Field Theory and the basics of Special Relativity is assumed.

 

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Contents

1 Vectors Tensors Manifolds and Special Relativity
1
2 Lagrangians Hamiltonians and Noethers Theorem
28
3 Relativistic Kinematics and Phase Space
47
4 Angular Distributions
57
5 Dirac Algebra
68
6 Dimensional Regularization Ultraviolet and Infrared Divergences
85
7 QED Renormalization
95
8 OneLoop Two and ThreePoint Functions
112
9 Massive Spin One and Renormalizable Gauges
141
10 Symmetries and Effective Vertices
157
11 Effective Field Theory
162
12 Optical Theorem
173
Appendix A Master Integral
179
Appendix B Renormalization Group Equations
183
Appendix C Feynman Rules for Derivative Couplings
188
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About the author (2015)

Victor Ilisie graduated in Physics in 2010 from the University of Valencia and in the following year obtained his Master’s Degree in Advanced Physics (branch: Theoretical Physics). He subsequently worked as a researcher at the University of Valencia and in 2014 and 2015 has been teaching courses on Classical Mechanics at the university, where he is completing a PhD within the framework of a project on “Particle Physics Phenomenology at the LHC and Flavour Factories”. He has also worked temporarily at Université Paris-Sud, Orsay, France and has a number of published papers to his name.

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