Wavelet approach to accelerator problems. II. Metaplectic wavelets

Abstract

This is the second part of a series of talks in which we present applications of wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to the orbit method and by using construction from the geometric quantization theory we construct the symplectic and Poisson structures associated with generalized wavelets by using metaplectic structure and corresponding polarization. The key point is a consideration of the semidirect product of the Heisenberg group and metaplectic group as subgroup of the automorphism group dual to the symplectic space, which consists of elements acting by affine transformations.