Supermanifolds, Theory and Applications

Question

Referee this paper: ISBN: 978-981-02-1228-5 by Alice Rogers

Please use comments to point to previous work in this direction, and reviews to referee the accuracy of the paper. Feel free to edit this submission to summarise the paper (just click on edit, your summary will then appear under the horizontal line)

(Is this your paper?)

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This book aims to fill the gap in the available literature on supermanifolds, describing the different approaches to supermanifolds together with various applications to physics, including some which rely on the more mathematical aspects of supermanifold theory.

The first part of the book contains a full introduction to the theory of supermanifolds, comparing and contrasting the different approaches that exist. Topics covered include tensors on supermanifolds, super fibre bundles, super Lie groups and integration theory.

Later chapters emphasise applications, including the superspace approach to supersymmetric theories, super Riemann surfaces and the spinning string, path integration on supermanifolds and BRST quantization.

Comments

The textbook "Supermanifolds, Theory and Applications" of Alice Rogers explains
super mathematics and its applications from a nicely "physicists-friendly" but nevertheless rigorous differential geometric point of view called the concrete approach to supermanifolds to which the author has contributed herself. For those who do not (yet?) speak the algebro-geometric language fluently it might be THE book about supermanifolds and their application in theoretical physics. However, the relationship to the algebro-geometric approach is also established in chapter 8 of the book and further detailled about the correspondance between the two points of view are derived in the author's 1980 Paper.

PS: Even though it is a textbook I gave it an upvote or originality too, because nowhere else have I seen the theory of supermanifolds explained and derived in such a nice detailled way from the differential geometric point of view ...

PPS: This comment might well be followed by an answer to the submission sometimes in the near future as soon as I am done putting it into the context of other literature concerning the subject ...