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Wavefront sets and polarizations on supermanifolds

Dappiaggi, Claudio; Gimperlein, Heiko; Murro, Simone; Schenkel, Alexander

Authors

Claudio Dappiaggi

Heiko Gimperlein

Simone Murro

Alexander Schenkel



Abstract

In this paper we develop the foundations for microlocal analysis on supermanifolds. Making use of pseudodifferential operators on supermanifolds as introduced by Rempel and Schmitt, we define a suitable notion of super wavefront set for superdistributions which generalizes Dencker's polarization sets for vector-valued distributions to supergeometry. In particular, our super wavefront sets detect polarization information of the singularities of superdistributions. We prove a refined pullback theorem for superdistributions along supermanifold morphisms, which as a special case establishes criteria when two superdistributions may be multiplied. As an application of our framework, we study the singularities of distributional solutions of a supersymmetric field theory.

Journal Article Type Article
Publication Date 2017-02
Journal Journal of Mathematical Physics
Print ISSN 0022-2488
Electronic ISSN 1089-7658
Publisher AIP Publishing
Peer Reviewed Peer Reviewed
Volume 58
Issue 2
Article Number 23504
APA6 Citation Dappiaggi, C., Gimperlein, H., Murro, S., & Schenkel, A. (2017). Wavefront sets and polarizations on supermanifolds. Journal of Mathematical Physics, 58(2), https://doi.org/10.1063/1.4975213
DOI https://doi.org/10.1063/1.4975213
Keywords Supermanifolds, Pseudodifferential operators, Polarized wavefront sets, Microlocal analysis, Propagation of singularities
Publisher URL https://doi.org/10.1063/1.4975213
Related Public URLs https://arxiv.org/abs/1512.07823
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Journal of Mathematical Physics 58, 023504 (2017); doi: 10.1063/1.4975213 and may be found at https://doi.org/10.1063/1.4975213

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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