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Supersymmetric Killing Structures

Supersymmetric Killing Structures In this text we combine the notions of supergeometry and supersymmetry. We construct a special class of supermanifolds whose reduced manifolds are (pseudo-) Riemannian manifolds. These supermanifolds allow us to treat vector fields on the one hand and spinor fields on the other hand as equivalent geometric objects. This is the starting point of our definition of supersymmetric Killing structures. The latter combines subspaces of vector fields and spinor fields, provided they fulfill certain field equations. This naturally leads to a superalgebra which extends the supersymmetry algebra to the case of non-flat reduced space. We examine in detail the additional terms which enter into this structure and we give a lot of examples. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematical Physics Springer Journals

Supersymmetric Killing Structures

Communications in Mathematical Physics , Volume 255 (2) – Feb 4, 2005

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References (40)

Publisher
Springer Journals
Copyright
Copyright © 2005 by Springer-Verlag Berlin Heidelberg
Subject
Physics; Theoretical, Mathematical and Computational Physics; Mathematical Physics; Quantum Physics; Complex Systems; Classical and Quantum Gravitation, Relativity Theory
ISSN
0010-3616
eISSN
1432-0916
DOI
10.1007/s00220-004-1277-2
Publisher site
See Article on Publisher Site

Abstract

In this text we combine the notions of supergeometry and supersymmetry. We construct a special class of supermanifolds whose reduced manifolds are (pseudo-) Riemannian manifolds. These supermanifolds allow us to treat vector fields on the one hand and spinor fields on the other hand as equivalent geometric objects. This is the starting point of our definition of supersymmetric Killing structures. The latter combines subspaces of vector fields and spinor fields, provided they fulfill certain field equations. This naturally leads to a superalgebra which extends the supersymmetry algebra to the case of non-flat reduced space. We examine in detail the additional terms which enter into this structure and we give a lot of examples.

Journal

Communications in Mathematical PhysicsSpringer Journals

Published: Feb 4, 2005

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