Supermatrix manifolds

Matrix manifolds are natural representation spaces of direct products of groups. Physical symmetries also appear in the form of direct products and, therefore, it may be of some interest to investigate the connection between the symmetry and the geometry of the representation space. In the present p...

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Bibliographic Details
Published in:Reports on mathematical physics 1991, Vol.29 (3), p.321-336
Main Author: Rzewuski, J.
Format: Article
Language:English
Subjects:
Exact sciences and technology
General theory of fields and particles
Physics
Symmetry and conservation laws
The physics of elementary particles and fields
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Summary:Matrix manifolds are natural representation spaces of direct products of groups. Physical symmetries also appear in the form of direct products and, therefore, it may be of some interest to investigate the connection between the symmetry and the geometry of the representation space. In the present paper the theory of matrix manifolds is generalized to supermatrix manifolds in view of their connection to direct products of supergroups. The analytical, geometrical and group-theoretical structure of these supermanifolds is described in some detail. In particular it is investigated how the manifolds decompose when the symmetry is reduced. An example corresponding to the physically plausible symmetry SU(2, 2; v, G )×SU( m,μ G ), containing the conformal as well as the Poincarè symmetry, is considered.
ISSN:0034-4877
1879-0674
DOI:10.1016/0034-4877(91)90050-W