Abstract

First the “frame problem” is sketched: The motion of an isolated particle obeys a simple law in Galilean frames, but how does the Galilean character of the frame manifest itself at the place of the particle? A description of vacuum as a system of virtual particles will help to answer this question. For future application to such a description, the notion of global particle is defined and studied. To this end, a systematic use of the Fourier transformation on the Poincaré group is needed. The state of a system of n free particles is represented by a statistical operator W, which defines an operator-valued measure on ^Pn (^P is the dual of the Poincaré group). The inverse Fourier–Stieltjes transform of that measure is called the characteristic function of the system; it is a function on Pn. The main notion is that of global characteristic function: it is the restriction of the characteristic function to the diagonal subgroup of Pn; it represents the state of the system, considered as a single particle. The main properties of characteristic functions, and particularly of global characteristic functions, are studied. A mathematical Appendix defines two functional spaces involved