The conceptual framework of quantum field theory. (Q2881854)

During the past seventy years there has been a steady stream of expository books aimed at introducing graduate students to the concepts of modern quantum field theory adequate to explore and start research in particle physics at the time. With such an amount of classic treatises one may well doubt the need for yet another book of quantum field theory. However, with each step in the development it is necessary anew to emphasize the reasons why such a theory should describe reality. So, why another book on quantum field theory in 2012? The book of Anthony Duncan, physics professor at the University of Pittsburgh, contains a good amount of new material and offers something new in content and contemporary perspective. In the Preface he cites many examples where important conceptual issues are not carefully explained in any of the readily available textbooks. An attempt is made to provide frequently neglected, nevertheless important concepts. The book is divided into four parts, entitled \textit{Origins}, \textit{Dynamics}, \textit{Symmetries}, and \textit{Scales}. The first part is historical which trace the evolution of modern QFT. The three other parts follow a step-by-step reconstruction of the entire framework beginning with relativistic invariance, the basic principles of quantum mechanics, and the prohibition of physical action at a distance. Subsequent chapters lay out the basic structure of QFT arising from quantum mechanics and relativistic as well as locality constraints. The classical limit is discussed in greater depth than usually found in standard texts. Answers are given to questions like: why do we need Lagrangians? Abelian and non-abelian gauge theories are discussed in great detail. In the final section features of QFT are explored that are most critical for their phenomenological success, i.e. the scale separation embodied by the renormalization group of theories defined by effective local Lagrangians. This book will be an invaluable modern reference text for physicists and mathematicians alike who use QFT in their research. But it is also an excellent textbook appropriate to graduate students.