The Penrose Transform: Its Interaction with Representation Theory (Dover Books on Mathematics) by Robert J. Baston | (PDF) Free Download

Description

“Brings to the reader a huge amount of information, well organized and condensed into less than two hundred pages.” — Mathematical ReviewsIn recent decades twistor theory has become an important focus for students of mathematical physics. Central to twistor theory is the geometrical transform known as the Penrose transform, named for its groundbreaking developer. Geared toward students of physics and mathematics, this advanced text explores the Penrose transform and presupposes no background in twistor theory and a minimal familiarity with representation theory. An introductory chapter sketches the development of the Penrose transform, followed by reviews of Lie algebras and flag manifolds, representation theory and homogeneous vector bundles, and the Weyl group and the Bott-Borel-Weil theorem. Succeeding chapters explore the Penrose transform in terms of the Bernstein-Gelfand-Gelfand resolution, followed by worked examples, constructions of unitary representations, and module structures on cohomology. The treatment concludes with a review of constructions and suggests further avenues for research.

User’s Reviews

Editorial Reviews: About the Author Robert J. Baston was on the faculty of The Mathematical Institute, University of Oxford. Michael G. Eastwood is Professor of Mathematics at the Mathematical Sciences Institute, Australian National University, Canberra.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Brilliant Dover Reprint of Classic. This book assumes familiarity with Twistor Theory and Representation Theory aka assumes knowledge of Abstract Algebra. Must have for Mathematical aka Theoretical Physicist interested in Twistor Theory.

⭐Great!

⭐Roger Penrose is well known to the educated public from his book, “The Emperor’s New Mind”, where he mused on the physical origin of consciousness. Whether you agreed with that or not, you should be aware that prior to that book, he was well reknowned in mathematics and theoretical physics.Penrose made his name with groundbreaking papers on twistor theory, where he posited a conformally invariant physics in the 4 dimensions of spacetime. He found a mapping between a field equation in physics and a projective space that was later called by others the Penrose Transform.This book extends that work by making a generalisation of the transform so that twistors can be applied to higher dimensional spaces. This may be of interest to you, if you study superstrings or supergravity. There, our mundane spacetime is subsumed in a much larger space.You need to be familiar with the theory of continuous groups and Dynkin diagrams to use this book. (Cf. Wybourne’s “Classical Groups for Physicists” for good preparation.) The level of development is quite advanced.

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