Poincaré Coherent States and Relativistic Phase Space Analysis

Abstract

Group theory is one of the cornerstones of wavelet analysis. Indeed, at a very general level, one may say that the following three concepts are equivalent: (i) a square integrable representation U of a group G; (ii) coherent states over G; (iii) the wavelet transform associated to U.This analysis is familiar in the two standard cases [1], which have been thoroughly discussed during this colloquium:

• (i) the affine (ax+b) group, which yields the usual wavelet analysis;

• (ii) the Weyl-Heisenberg group, which leads to various phase space or time-frequency representations.