The Wigner caustic on shell and singularities of odd functions
Mathematical Physics
2014-11-17 v3 math.MP
Symplectic Geometry
Abstract
We study the Wigner caustic on shell of a Lagrangian submanifold L of affine symplectic space. We present the physical motivation for studying singularities of the Wigner caustic on shell and present its mathematical definition in terms of a generating family. Because such a generating family is an odd deformation of an odd function, we study simple singularities in the category of odd functions and their odd versal deformations, applying these results to classify the singularities of the Wigner caustic on shell, interpreting these singularities in terms of the local geometry of L.
Cite
@article{arxiv.1207.1068,
title = {The Wigner caustic on shell and singularities of odd functions},
author = {Wojciech Domitrz and Miriam Manoel and Pedro de M. Rios},
journal= {arXiv preprint arXiv:1207.1068},
year = {2014}
}
Comments
24 pages