Wavefront sets and polarizations on supermanifoldsTools Dappiaggi, Claudio and Gimperlein, Heiko and 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 Full text not available from this repository.
Official URL: https://doi.org/10.1063/1.4975213
AbstractIn 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.
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