Friday, July 1, 2011

From Special Relativity to Feynman Diagrams (UNITEXT / Collana di Fisica e Astronomia)

From Special Relativity to Feynman Diagrams (UNITEXT / Collana di Fisica e Astronomia)

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The first two chapters of the book deal, in a detailed way, with relativistic kinematics and dynamics, while in the third chapter some elementary concepts of General Relativity are given.Eventually, after an introduction to tensor calculus, a Lorentz covariant formulation of electromagnetism is given its quantization is developed.For a proper treatment of invariance and conservation laws in physics, an introductory chapter on group theory is given. This introduction is propedeutical to the discussion of conservation laws in the Lagrangian and Hamiltonian formalism, which will allow us to export this formalism to quantum mechanics and, in particular, to introduce linear operators on quantum states and their transformation laws. In the last part of the book we analyze, in the first quantized formalism, relativistic field theory for both boson and fermion fields. The second quantization of free fields is then introduced and some preliminary concepts of perturbation theory and Feynmann diagrams are given and some relevant examples are worked out.

From Special Relativity to Feynman Diagrams (UNITEXT / Collana di Fisica e Astronomia) Review

This is definitely an exceptional book covering most of the basic divisions of modern physics concisely yet in a stunningly deep and insightful fashion. I would never expect, and have never seen that so much of advanced topics could be gathered in a single moderate volume with such a depth. Chapters 1&2, covering the special relativity, is almost a masterpiece in itself. The conciseness does never prevent the authors from conveying to you their deep insight. Almost the same continues in their presentation of; Symmetry and Lie Groups, Lagrangian and Hamiltonian formalism, Electromagnetic field and its quantization, which is an early and basic introduction to quantum field theory, Non-relativistic and relativistic quantum mechanics and finally Quantum field theory. General Relativity is given a relatively short and passing touch, yet here also the presentation of the basic equivalence principle is unique. On my part, I have experienced the delight and satisfaction of finding answers to some questions bothered me for long times. Finally, arriving to a basic understanding, albeit at an introductory level, of what quantum field theory is, and why it is needed in the first place, is an exceptional joy in itself. Not a physicist by profession, this is sufficient for me. Others may built on and continue as far as they wish after persevering in the study of this book from start to the end.

Having covered almost all of foundations of modern physics with full definitions given from the scratch, the authors have created a body of text, which is very coherent in its flow and logic. Thus, in my idea, any one having some maturity in philosophy of science, classical mechanics and electromagnetism, with an introduction to special relativity and quantum mechanics (at an undergraduate level) can, theoretically, tackle this beautiful book; of course with hard work, zeal and perseverance. It is a monograph without any problems and exercises. But this is more than compensated if one fills in the slipped steps in derivations and conclusions reached. Similarly one should think hard on some hints and allusions as well as convince himself about the insightful remarks and judgments, generously presented. I attribute the shortness of references list to the self sufficiency of the book. I have all of the books in this list, but would compare none of them with this one.

The well-known Jacoby identity for the Poison Brackets, given on page 225 is obviously a typo the correct form of which is already given in Annex D.

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