2001/06/25 by J. Y. Grandpeix, F. Lurcat
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP
published as Found.Phys. 32 (2002) 109-131 · 17 pages, no figure, LaTeX2e, Submitted to Foundation of Physics
arxiv created 2001/06/25 · arxiv updated 2009/11/30
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 Poincare 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 the n-th power of the dual of the Poincare group. The inverse Fourier-Stieltjes transform of that measure is called the characteristic function of the system; it is a function on the n-th power of the Poincare group. The main notion is that of global characteristic function: it is the restriction of the characteristic function to the diagonal subgroup ; 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.