Twistor Geometry and Field Theory (Cambridge Monographs on Mathematical Physics)

Rating:
Summary: Serving both mathematicians and physicists
Review: Although Twistor theory has not achieved its initial goal of quantizing Einstein's General Relativity, the field has discovered other useful results in both pure mathematics and classical / quantum field theory. This monograph cleanly presents the mathematical foundation of Penrose's Twistor theory in the first part of the book. The second part of the text describes field theory in detail with special focus on application of Twistor methods to instatons in Yang Mills theory and Einstein's gravity. There are almost no other texts in the market presenting analysis of these subjects; therefore this monograph fills a crucial gap.

Written by mathematicians, the text presents material in a fashion only slightly more rigorous then usual for physicists but still in an accomidating manner. Surprisingly, the physical arguments presented in the section on field theory are sharply written and so could prove useful to mathematicians interested in learning field theory.

Overall this is a lucidly written document that serves a unique role.

Rating:
Summary: beautifully written
Review: From the mathematical point of view, this is an enjoyable read; it could even serve as a first exposure to algebraic topology.

It is without question that Penrose's remarkable insights have come a long way in helping physicists foster new mathematical ideas, and putting them on solid footing; and this is what the authors have set out to do. It is written in a very clear and lucid style, and it is the most comprehensive expository work in mathematical physics that I have seen in a long time.
-A

Rating:
Summary: A model of clarity
Review: This is an extremely well written book. Couldn't be more clear. The authors derserve an AMS award for clarity of exposition. They even explain to physicists (read mathematical idiots) what a sheaf cohomolgy is. Hats raised to their efforts.