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Super geometry

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Reflections on Quanta, Symmetries, and Supersymmetries

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Abstract

Supersymmetry was discovered by physicists around 1970. At first it was just a device for treating the bosonic and fermionc aspects of quantum statistical mechanics and quantum field theory on an equal footing. Eventually, due to the remarkable ideas and contributions of many physicists and mathematicians, supersymmetry came to be understood as the symmetry of a new kind of geometrical object, namely, a super manifold. The super manifolds are objects in super geometry, which is a deep generalization of conventional differential and algebraic geometry. The symmetries of super manifolds form super Lie groups.

This essay and the next are based on various articles and lectures on supersymmetry I have given on many an occasion, especially a series of lectures in the Courant Institute in New York, in 2002, and in Oporto, Portugal, in 2006. I am extremely grateful to the large number of people with whom I have discussed the issues that form the core of these essays, and from whom I learnt most of the things I talk about. I would like to mention many notably Luigi Balduzzi, Claudio Carmeli, Gianni Cassinelli, Lauren Caston, Pierre Deligne, Sergio Ferrara, Rita Fioresi, Marian Lledo, Albert Schwarz, and Alessandro Toigo, to mention just a few. See also [1].

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Authors and Affiliations

  1. Department of Mathematics, University of California, 90095-1555, Los Angeles, CA, USA

    V. S. Varadarajan

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Varadarajan, V.S. (2011). Super geometry. In: Reflections on Quanta, Symmetries, and Supersymmetries. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0667-0_4

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