The conceptual framework of quantum field theory - Duncan, Anthony , (Professor of physics) (Oxford University Press, 2012)
Includes bibliographical references (pages [765]-776) and index
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
Origins I: from the arrow of time to the first quantum field -- Origins II: gestation and birth of interacting field theory: from Dirac to Shelter Island -- Dynamics I: the physical ingredients of quantum field theory: dynamics, symmetries, scales -- Dynamics II: quantum mechanical preliminaries -- Dynamics III: relavistic quantum mechanics -- Dynamics IV: aspects of locality: clustering, microcausality, and analyticity -- Dynamics V: construction of local covariant fields -- Dynamics VI: the classical limit of quantum fields -- Dynamics VII: interacting fields: general aspects -- Dynamics VIII: interacting fields: perturbative aspects -- Dynamics IX: interacting fields: non-perturbative aspects -- Dynamics IX: interacting fields: non-perturbative aspects -- Symmetries I: continuous spacetime symmetry: why we need Lagrangians in field theory -- Symmetries II: discrete spacetime symmetries -- Symmetries III: global symmetries in field theory -- Symmetries IV: local symmetries in field theory -- Scales I: scale sensitivity of field theory amplitudes and effective field theories -- Scales II: perturbatively renormalizable field theories -- Scales III: short-distance structure of quantum field theory -- Scales IV: long-distance structure of quantum field theory -- Appendix A: the functional calculus -- Appendix B: Rates and cross-sections -- Appendix C: Majorana spinor algebra