Wavefront sets and polarizations on supermanifolds

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

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.

Citation

Dappiaggi, C., Gimperlein, H., Murro, S., & Schenkel, A. (2017). Wavefront sets and polarizations on supermanifolds. Journal of Mathematical Physics, 58(2), Article 23504. https://doi.org/10.1063/1.4975213

• Journal Article Type: Article
• Acceptance Date: Jan 18, 2017
• Online Publication Date: Feb 13, 2017
• Publication Date: 2017-02
• Deposit Date: Mar 2, 2017
• Publicly Available Date: Mar 2, 2017
• Journal: Journal of Mathematical Physics
• Print ISSN: 0022-2488
• Electronic ISSN: 1089-7658
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 58
• Issue: 2
• Article Number: 23504
• DOI: https://doi.org/10.1063/1.4975213
• Keywords: Supermanifolds, Pseudodifferential operators, Polarized wavefront sets, Microlocal analysis, Propagation of singularities
• Public URL: https://nottingham-repository.worktribe.com/output/846028
• Publisher URL: https://doi.org/10.1063/1.4975213
• Related Public URLs: https://arxiv.org/abs/1512.07823
• 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
• Contract Date: Mar 2, 2017