Conceptual Framework of Quantum Field Theory

The book attempts to provide an introduction to quantum field theory emphasizing conceptual issues frequently neglected in more "e;utilitarian"e; treatments of the subject. The book is divided into four parts, entitled respectively "e;Origins"e;, "e;Dynamics"e;, "e;Symmetries"e;, and "e;Scales"e;. The emphasis is conceptual - the aim is to build the theory up systematically from some clearly stated foundational concepts - and therefore to a large extent anti-historical, but two historical Chapters ("e;Origins"e;) are included to situate quantum field theory in the larger context of modern physical theories. The three remaining sections of the book follow a step by step reconstruction of this framework beginning with just a few basic assumptions: relativistic invariance, the basic principles of quantum mechanics, and the prohibition of physical action at a distance embodied in the clustering principle. The "e;Dynamics"e; section of the book lays out the basic structure of quantum field theory arising from the sequential insertion of quantum-mechanical, relativistic and locality constraints. The central role of symmetries in relativistic quantum field theories is explored in the third section of the book, while in the final section, entitled "e;Scales"e;, we explore in detail the feature of quantum field theories most critical for their enormous phenomenological success - the scale separation property embodied by the renormalization group properties of a theory defined by an effective local Lagrangian.