An Invitation to Quantum Field Theory

This fresh approach to teaching Quantum Field Theory examines challenging concepts with a minimum of technical detail. The book treats the discussion of the main ideas as more important than the presentation of technical mathematical details.

This book provides an introduction to Quantum Field Theory (QFT) at an elementary level—with only special relativity, electromagnetism and quantum mechanics as prerequisites. For this fresh approach to teaching QFT, based on numerous lectures and courses given by the authors, a representative sample of topics has been selected containing some of the more innovative, challenging or subtle concepts. They are presented with a minimum of technical details, the discussion of the main ideas being more important than the presentation of the typically very technical mathematical details necessary to obtain the final results. Special attention is given to the realization of symmetries in particle physics: global and local symmetries, explicit, spontaneously broken, and anomalous continuous symmetries, as well as discrete symmetries. Beyond providing an overview of the standard model of the strong, weak and electromagnetic interactions and the current understanding of the origin of mass, the text enumerates the general features of renormalization theory as well as providing a cursory description of effective field theories and the problem of naturalness in physics. Among the more advanced topics the reader will find are an outline of the first principles derivation of the CPT theorem and the spin-statistics connection. As indicated by the title, the main aim of this text is to motivate the reader to study QFT by providing a self-contained and approachable introduction to the most exciting and challenging aspects of this successful theoretical framework.

Why Do We Need Quantum Field Theory After All?.- From Classical to Quantum Fields.- Theories and Lagrangian I: Matter Fields.- Theories and Lagrangian II: Introducing Gauge Fields.- Theories and Lagrangian II: The Standard Model.- Towards Computational Rules: Feynman Diagrams.- Symmetries I: Continuous Symmetries.- Renormalization.- Anomalies.- The Origin of Mass.- Symmetries II: Discrete Symmetries.- Effective Field Theories and Naturalness.- Special Topics.- Notation, Conventions and Units.- A Crash Course in Group Theory.- Index.