Gauge Field Theory and Complex Geometry

From the reviews: "The mathematical level is rather advanced and is focused mainly on complex differential geometry and holomorphic bundle theory... This is a powerful book, written by a very distinguished contributor to the field..." (Contemporary Physics )"... the book provides a large amount of background for current research across a spectrum of field. ... requires effort to read but it is worthwhile and

• From the contents: The subject of the book is an expositon of two new ideas in Math. Phys.: that of twistors and that of supersymmetry. The exposition is geometrized and unified. Applications to the solution of nonlinear differential equations of quantum field theory are given, in particular, to the theory of instantons. The exposition is largely based upon the results of the author, published in physical magazins. The second part of the book, Ch. 3 and 4, contain a mathematical introduction to superalgebra and supergeometry, which can be read independently and used by students in algebra and geometry. For the first time in mathematical literature an introduction to the geometry of supergravity is given. Methods of complex geometry, in particular sheaf cohomology, are used throughout. Since the newest quantum field theory, dealing with (super)unification schemes and (super)strings uses more and more of complex geometry, this book may serve to introduce both physicists and mathematicians to this quickly expanding new domain.