## Sunday, October 15, 2006

### "PCT, Spin and Statistics, and All That" by Raymond F. Streater

Obsolete and full of incorrect statements

The review has been erased by organized cranks. I post a copy on my weblog.

Many new discoveries and advances in particle physics and quantum field theory have been made since 1964, the year when this book was originally published. In the 1960s, this book might have been a legitimate attempt to establish a new, albeit controversial paradigm in the research of Quantum Field Theory. However the authors were not too lucky because now, exactly 40 years later, we see that Axiomatic Field Theory has not led anywhere, unlike the specific, constructive, and old-fashioned quantum field theories. Axiomatic Field Theory has given no physical predictions and it has led to no conceptual developments. Today, Axiomatic Field Theory is not an active field of physics anymore. Moreover, most of its conclusions are believed to be incorrect.

Of course, I don't mean the CPT theorem. But the CPT theorem and the relation of statistics and spin has become a miniscule portion of our current knowledge about quantum field theory and no one should spend so much money for a book that presents these things in such an obsolete fashion.

Although some sections of the book may sound familiar and they are remotely related to some topics in contemporary physics, the book does not cover the most essential parts of current quantum field theory - such as gauge theories, path integrals, Higgs mechanism, confinement, asymptotic freedom, renormalization group, dualities, solitons (except for a few pages in the appendix), instantons, semiclassical treatment of quantum gravity, supersymmetry, string theory, and many others - and even the topics that the book tries to cover are described in a confusing way. For example, a reader has "learned" from this book that one can always define the parity operator, which everyone else today knows to be wrong, and so on.

The discovery of the Renormalization Group (RG) showed that many exact - and seemingly rigorous - ideas about the operator algebras were too naive to be true. Today, a realistic quantum field theory must be given a distance scale, and all quantities are calculated with respect to this scale. There exists almost no useful quantum field theory that would satisfy the axioms of Axiomatic Field Theory, and therefore the "theorems" derived within the framework of Axiomatic Field Theory have almost no physical impact. The only exception where the axiomatic approach had some successes seem to be the conformal field theories in two dimensions but they are not presented in this book either.

Although there are many correct and useful statements in the book, the number of incorrect and misleading sections is too large and it makes the book useless. There are much better recent books written at a comparable level of difficulty, e.g. "Quantum Field Theory in a Nutshell" by Anthony Zee.