Quantum Field Theory (International Series in Pure and Applied Physics) [Hardcover]

However, it's strongest selling point is the fact that it actually works out examples in incredible detail - where else do you find a complete computation of a two loop vacuum polarization amplitude? This is the ideal book for someone who actually wants to learn how to do calculations in field theory.

It has two shortcomings - it was written in the 80's so it isn't very modern and it has no problems. But those pale in light of its advantages.

Some of the highlights of the book include: 1. The "wave packet" solution of the Dirac equation and the Zitterbewegung phenomenon, which the authors use as a counterexample to the idea of treating negative energy states in the framework of a 1-particle theory. 2. The treatment of two-body relativistic corrections to study the recoil of the nucleus, this being done in the context of the Dirac equation. 3. The use of the Dirac hole theory to motivate the need for a true many-body theory to accomodate particles and antiparticles via quantized fields. 4. A fairly lengthy discussion of the Fock-Schwinger proper time method to obtain an exact expression for the Dirac propagator in a constant uniform electromagnetic field and a plane wave electromagnetic field. 5. The discussion on the use of coherent states to study the positive frequency part of a (free) quantum field. 6. The discussion on charged scalar fields, and why they are needed to formulate a (scalar) theory of particles and antiparticles. 7. The quantization of the electromagnetic field using the Gupta-Bleuler method using an indefinite metric, and the need for retaining the full Fock space (with indefinite norm) in order to preserve locality. 8. The discussion of the vacuum fluctuations via the Casimir effect. 9. The treatment of the Dirac field and the Pauli exclusion principle. The authors begin with two complex fields that both satisfy the Dirac equation, but the Lagrangian then vanishes. They thus are careful to note that canonical quantization will not work, and so they turn to the using their transformation laws under the Poincare group. The derivation of the anticommutators is purely heuristic (and they note this), and they point out that locality would not be satisfied if canonical quantization were followed. The same holds true, as they state also, if one were to quantize a scalar theory according to Fermi statistics. Their discussion here is a neat illustration of the spin-statistics theorem. 10. The discussion of form factors, which they motivate by calling them a relativistic generalization of charge distributions. 11. The discussion of the Euler-Heisenberg effective Lagrangian, and its ability, even though it is "classical", to model nonlinear phenomena due to quantum corrections. 12. The discussion of the Jost-Lehmann-Dyson representation. 13. The discussion of Euclidean Green functions. 14. The derivation of the Ward-Takahashi identities and the proof that they are preserved by the regularization and renormalization operations. 15. The discussion on functional integration in Bargmann-Fock space, in particular its use in fermion systems. 16. The discussion of the Schwinger-Dyson equations and their use in studying quantum field theory independent of perturbation theory. The existence of a bound state in quantum field theory has yet to be proven using these equations, but they supposedly hold the answer to this existence. The authors give an example of scalar particles interacting via the exchange of scalar particles via the Bethe-Salpeter equation, which are then studied via Wick rotation and where crossed-ladder diagrams are omitted. They also analyze the hyperfine splitting in positronium, but remark that the methods used for this are not entirely satisfactory. 17. The discussion of the sigma model, a topic that has become very important of late. 18. The discussion of asymptotic behavior, the authors emphasizing how the infinities in the relation between bare and renormalized charges and how these infinities must compensate imposes constraints on the theory, which show up in the asymptotic behavior.

Some of the omissions which might be expected from a modern standpoint: 1. Representations of the Poincare group. 2. Critical phenomena. 3. Integrable systems in quantum field theory 4. Finite temperature quantum field theory. 5. Quantum field theory in curved spacetime. 6. A more in-depth treatment of instantons (the authors only spend one page on them). 7. Topological quantum field theory.

It is too bad that it is no longer in print. I was fortunate enough to buy a copy when it was still on the shelves. I would imagine though that almost every scientific library would have copy.