Wavefront sets and polarizations on supermanifolds

作者：Dappiaggi Claudio^*; Gimperlein Heiko; Murro Simone; Schenkel Alexander

来源：Journal of Mathematical Physics, 2017, 58(2): 023504.

DOI：10.1063/1.4975213

In this paper, we develop the foundation 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. Published by AIP Publishing.

• 出版日期2017-2