Physics Science

This book is a fine one, and it emphasizes the practical aspects of quantum field theory rather than the abstract formalism. The author has written a book that would be of use to the graduate student in physics who is intending to specialize in quantum field theory or experimental particle physics.

The book is divided into four parts. The author begins in part one with an overview of the quantization of the vibrating string via canonical quantization. This method involves finding the normal modes of the string, and then replacing the canonical variables with operators that satisfy particular non-commutation relations. The resulting structure is interpreted as a phonon field (in the particle picture). The author gives an interesting and detailed discussion of field-particle duality by taking the classical limit, and one can see clearly the origin of the famous coherent states.

Part one is also an introduction to quantum electrodynamics. The author discusses the quantization of the electromagnetic field as a quantization problem with constraints, the latter being gauge and Lorentz invariance. The conflict between these two requirements is illustrated by the choice of different gauges, such as the Coulomb gauge (which is not manifestly covariant). The interaction picture also makes its appearance, wherein the S-matrix is derived, and the Lamb shift is calculated and compared with experiment. The famous mass renormalization problem is discussed, and the cross section for deuteron photodisintegration is calculated. This calculation is interesting in that detailed knowledge of the strong interaction is not necessary to obtain the correct answer.

Part two of the book is an overview, with historical emphasis, of the Klein-Gordon and Dirac equations. The reader can see the origin here of the concept of a quantum field, but a full understanding of these fields is not yet available in modern physics, particularly in the utility of these fields in predicting bound states. The Klein-Gordon equation is interpreted as a description of a charged particle, with its norm the charge density, and a solution of the Klein-Gordon equation equation is given, involving pair creation from a high Coulomb barrier. This example is interesting in that it predicts negative energy states in the context of the Klein-Gordon equation, and is not done in any other textbooks in quantum field theory. The non-relativistic limits of both of these equations is discussed, and applications given, such as the Zeeman effect. The author also shows that the homogeneous Lorentz group is not simply-connected, and proves the covariance of the Dirac equation by constructing a representation of the Lorentz group on (four-dimensional) Dirac space, i.e. the space of spinors. The author also gives an introduction to hadron physics, via the MIT bag model. All of these discussions are interesting but they leave the reader wanting for an explanation of how bound states can form in a fully relativistic quantum field theory.

In part three, the author delves more deeply into the theoretical aspects of quantum field theory, and proves the famous PCT theorem. Such a discussion will prepare the reader for an understanding of the current theories regarding mirror matter. Interactions in quantum field theory are introduced via the phi-3 field theory, and the reader gets a first taste of the famous Feynman rules. One topic noticeably missing in this part is that of effective field theories. This is a topic of enormous importance in current formulations of quantum field theories and their connection with other theories of fundamental interactions, such as string theories. Such a discussion would be appropriate in this part, particularly in the sections on pion-nucleon interactions. An entire chapter is spent on renormalization, wherein Wick’s theorem is proved. A mathematically-astute reader will find the idea of renormalization troubling from a mathematical point of view, but a more rigorous foundation for renormalization does currently exist in the literature. The problem of bound states in quantum field theory is dealt with in this part by the partial summing of particular Feynman diagrams, the so-called ladder and crossed ladder sums of Feynman diagrams. This leads to the famous Bethe-Salpeter equation and the author’s “spectator” equation. The author shows the equivalence of these approaches in dealing with the (two-body) bound state problem. In addition, he also introduces briefly the Blackenbecler-Sugar equation as another relativistic two-body equation, but does not compare this equation to the other approaches at all. The Schwinger-Dyson equations would be the natural thing to discuss in this part, and how one might derive the relativistic two-body equations from them, but the author does not do so, unfortunately.

The last part is on overview of quantum gauge theories. Gauge symmetry is introduced as a “dynamical” symmetry, which, the author argues is strong enough to be able to determine the structure of the Lagrangian of the theory. This strategy is one of the most pervasive in all modern attempts at building unified theories of particle interactions. He also does give an introduction to chiral symmetry, in the context of the strong interaction. The discussion of chirality is unfortunately the only example of an effective field theory in the book. The method of functional integration is introduced to deal with the quantization of gauge theories, and the reader can see the origin of the famous Faddeev-Popov ghosts. The electroweak model, the most successful of the Non-abelian gauge theories to this date, is also discussed in fair detail. Examples of the calculation of cross sections for the intermediate vector bosons are not included though, surprisingly. The book ends with a fairly detailed discussion of the renormalization group and asymptotic freedom. The later property of the gauge theory of the strong interaction is definitely a confidence builder in one’s belief that gauge theories contain a hint of the correct physics for the strong interaction.
Rating: 4 / 5

Unusually clear and practical, with alot of examples. Includes topics not available elsewhere, including relativistic three body problems, and bound state wavefunctions derived from field theory.
Rating: 5 / 5

I thought this book was more elementary because its title says Relativistic QUANTUM MECHANICS and Field Theory. Well, it is not.

The Quantum Mechanics part is brief and the Quantum Field part is long and hard.

The chapter about relativistic bound-state theory is a plus not easily found in others Quantum Mechanics/Field books. The approach used is Field, not Mechanics, so its hard to follow what the author is doing. No applications will be found, like the positronium levels of energy or the quark confinement.

Dr Gross book, in general, is above my level of competence, so I stop here.

Rating: 4 / 5