Fundamental Interactions : A Roadmap to Classical and Quantum Field Theories

This book offers a modern and accessible introduction to the quantum–relativistic world of fundamental interactions. It presents advanced concepts in a clear and structured way, combining detailed calculations with intuitive explanations of core ideas. Written in a concise and contemporary style, the book adopts interactive teaching approaches to support active learning. A wide range of exercises, including standard problems, open-ended questions, and discussion topics, helps readers consolidate and deepen their understanding. The material is organized into twelve chapters divided into three conceptual parts. The first part introduces classical field theory, covering relativistic frameworks, symmetries, spin, and the basic elements of group theory. The second part focuses on quantum field theories and the relationship between fields and particles, including bosons and fermions, together with their relativistic quantum description. It also addresses several open challenges in modern theoretical physics, such as symmetry breaking, topological phenomena, the role of quasiparticles, and the nature of interactions, with particular attention to the properties of the S-matrix in quantum mechanics and quantum field theory. The final part examines particles and interactions in greater detail, presenting electromagnetism as a prototype theory and discussing its extensions and modern developments. Connections to the Standard Model and gravity are explored as frontier topics. Taken together, the chapters provide a clear and compact overview of the fundamental interactions, bridging classical and quantum perspectives. This book is intended for students who have completed introductory courses in classical mechanics, relativity, and quantum mechanics, typically during the first three years of a bachelor’s degree. It is well suited for readers seeking a coherent introduction to relativistic quantum theory and quantum field theory.