The Conceptual Framework of Quantum Field Theory

The book attempts to provide an introduction to quantum field theory emphasizing conceptual issues frequently neglected in more "utilitarian" treatments of the subject. The book is divided into four parts, entitled respectively "Origins", "Dynamics", "Symmetries", and "Scales". 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("Origins") 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 ofquantum mechanics, and the prohibition of physical action at a distance embodied in the clustering principle. The ''Dynamics" 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 "Scales", we explore in detail the feature ofquantum 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.

Part I: Origins
1. From the Arrow of Time to the First Quantum Field
2. Gestation and Birth of Interacting Field Theory- From Dirac to Shelter Island
Part II: Dynamics
3. The Physical Ingredients of Quantum Field Theory - Dynamics, Symmetries, Scales
4. Quantum Mechanical Preliminaries
5. Relativistic Quantum Mechanics
6. Aspects of Locality - Clustering, Microcausality, and Analyticity
7. Construction of Local Covariant Fields
8. The Classical Limit of Quantum Fields
9. Interacting Fields- General Aspects
10. Interacting Fields- Perturbative Aspects
11. Interacting Fields - Nonperturbative Aspects
Part III: Symmetries
12. Continuous Space-time Symmetry - Why we need Lagrangians in Field Theory
13. Discrete Space-time Symmetries
14. Global Symmetries in Field Theory
15. Local Symmetries in Field Theory
Part IV: Scales
16. Scale Sensitivity of Field Theory Amplitudes and Effective Field Theories
17. Perturbatively Renormalizable Field Theories
18. Short-distance Structure of Quantum Field Theory
19. Long-distance Structure of Quantum Field Theory