Causality and propagation in the Wigner, Husimi, Glauber, and Kirkwood phase-space representations - art. no. 052114

Time evolution is considered in phase space in terms of evolution kernels f or various phase-space quasi-distributions. The propagators for the Wigner function, the standard-ordered function, the Kirkwood (antistandard-orderd) function, the Glauber P and Q functions, and the Husimi function an explic itly written as bilinear transforms of the evolution operator. Free propaga tion propagation in dispersive media, and scattering, are studied, and mani festations of causality and interference are analyzed. It is shown that fre e propagation and scattering in the Husimi, Glauber, and Kirkwood represent ations with the underlying dynamics of the Schrodinger equation involve div ergent evolution kernels connecting distant phase-space points at all times . The time evolution is much simpler in the Wigner representation where (i) free propagation is a simple classical translation involving no interferen ce, and (ii) analytical properties of the scattering matrix restrict the ve locities of propagation so that no information can travel due to scattering faster than free motion. As an example, a correlation is found between the coordinate and momentum of particles detected after they are released from a box. Propagators with relativistic dispersion relations of free photons or Klein-Gordon particles an briefly discussed in an Appendix.