Wavefront sets and polarizations on supermanifolds
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 polarizatio...
| Main Authors: | , , , |
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| Format: | Article |
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American Institute of Physics
2017
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| Online Access: | https://eprints.nottingham.ac.uk/41001/ |
| _version_ | 1848796175228993536 |
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| author | Dappiaggi, Claudio Gimperlein, Heiko Murro, Simone Schenkel, Alexander |
| author_facet | Dappiaggi, Claudio Gimperlein, Heiko Murro, Simone Schenkel, Alexander |
| author_sort | Dappiaggi, Claudio |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:43:48Z |
| format | Article |
| id | nottingham-41001 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:48Z |
| publishDate | 2017 |
| publisher | American Institute of Physics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-410012020-05-04T18:34:54Z https://eprints.nottingham.ac.uk/41001/ Wavefront sets and polarizations on supermanifolds Dappiaggi, Claudio Gimperlein, Heiko Murro, Simone Schenkel, Alexander 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. American Institute of Physics 2017-02-13 Article PeerReviewed Dappiaggi, Claudio, Gimperlein, Heiko, Murro, Simone and Schenkel, Alexander (2017) Wavefront sets and polarizations on supermanifolds. Journal of Mathematical Physics, 58 (2). 23504/1-23504/16. ISSN 1089-7658 Supermanifolds Pseudodifferential operators Polarized wavefront sets Microlocal analysis Propagation of singularities https://doi.org/10.1063/1.4975213 doi:10.1063/1.4975213 doi:10.1063/1.4975213 |
| spellingShingle | Supermanifolds Pseudodifferential operators Polarized wavefront sets Microlocal analysis Propagation of singularities Dappiaggi, Claudio Gimperlein, Heiko Murro, Simone Schenkel, Alexander Wavefront sets and polarizations on supermanifolds |
| title | Wavefront sets and polarizations on supermanifolds |
| title_full | Wavefront sets and polarizations on supermanifolds |
| title_fullStr | Wavefront sets and polarizations on supermanifolds |
| title_full_unstemmed | Wavefront sets and polarizations on supermanifolds |
| title_short | Wavefront sets and polarizations on supermanifolds |
| title_sort | wavefront sets and polarizations on supermanifolds |
| topic | Supermanifolds Pseudodifferential operators Polarized wavefront sets Microlocal analysis Propagation of singularities |
| url | https://eprints.nottingham.ac.uk/41001/ https://eprints.nottingham.ac.uk/41001/ https://eprints.nottingham.ac.uk/41001/ |