Mathematical foundations of supersymmetry. (English) Zbl 1226.58003

Carmeli, Claudio; Caston, Lauren; Fioresi, Rita

EMS Series of Lectures in Mathematics. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-097-5/pbk). xiii, 287 p. (2011).

This is an excellent book. Supersymmetry is the machinery that physicists and mathematicians have developed to treat two types of elementary particles, bosons and fermions. Today supersymmetry plays an important role in high energy physics. Supergeometry and super Lie theory are the basis for supersymmetry. This monograph has grown out of the desire to present a moderately brief and focused account of the mathematical foundations of supersymmetry both in the differential and algebraic categories. The authors did not intend to give an encyclopedic treatment of supersymmetry but to supply only the foundational material that will allow the reader to penetrate the more advanced papers in the wide literature on this subject. This book is rich in content, and clear in argument. This book can very well be used as a one-semester course or a seminar on supersymmetry, directed to second and third year graduate students.

Reviewer: Chen Yong-Qing (Shenzhen)

MSC:

58A50	Supermanifolds and graded manifolds
58-02	Research exposition (monographs, survey articles) pertaining to global analysis
58C50	Analysis on supermanifolds or graded manifolds
14M30	Supervarieties
17A70	Superalgebras
32C11	Complex supergeometry
81Q60	Supersymmetry and quantum mechanics
22E70	Applications of Lie groups to the sciences; explicit representations

Keywords:

supersymmetry; supergeometry; super Lie theory