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Field Theories on Supermanifolds: General Formalism, Local Supersymmetry, and the Limit of Global Supersymmetry

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Topological Properties and Global Structure of Space-Time

Part of the book series: NATO ASI Series

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Abstract

The aim of this paper is to report briefly on recent investigations concerning the formulation of field theories on supermanifolds. The motivation of this research is twofold. On one hand, the usual formulations of “superspace field theories”, see e.g. Ref.1, are highly unsatisfactory from a mathematical viewpoint. The main criticisms that can be aroused are: (i) in classical (non-quantum) supersymmetric field theories spinor components have to be anticommuting c-numbers (?); (ii) superspace2 is defined formally (for instance, general coordinate transformations are mathematically not well defined). As a consequence, there is no room for studying global (topological) properties of superspace; (iii) most manipulations (e.g. the derivation of field equations from a variational principle) are merely formal.

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Author information

Authors and Affiliations

  1. Istituto di Matematica, Università di Genova, Via L. B. Alberti 4, 16132, Genova, Italy

    Ugo Bruzzo

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  1. Ugo Bruzzo
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Editor information

Editors and Affiliations

  1. Syracuse University, Syracuse, New York, USA

    Peter G. Bergmann

  2. New York University, New York, New York, USA

    Peter G. Bergmann

  3. University of Bologna, Bologna, Italy

    Venzo De Sabbata

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© 1986 Springer Science+Business Media New York

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Bruzzo, U. (1986). Field Theories on Supermanifolds: General Formalism, Local Supersymmetry, and the Limit of Global Supersymmetry. In: Bergmann, P.G., De Sabbata, V. (eds) Topological Properties and Global Structure of Space-Time. NATO ASI Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3626-4_3

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  • DOI: https://doi.org/10.1007/978-1-4899-3626-4_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-3628-8

  • Online ISBN: 978-1-4899-3626-4

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