Interacting Fock spaces related to the Anderson model

A new type of interacting Boltzmannian Pock space, emerging from the stocha stic limit of the Anderson model, is investigated. We describe the structur e of the space and the form, assumed in this case, by the principles of fac torization and of total connection. Using these principles, the vacuum expe ctation of any product of creation and annihilation operators can be calcul ated. By means of these results, for any test function, a system of differe nce equations satisfied by the moments of the field operator and an integra l equation satisfied by their generating function is deduced. In many inter esting cases this equation is solved and the vacuum distribution function o f the field operator (even its density) is explicitly determined. This evid entiates a new phenomenon which cannot take place in the usual Fock spaces land did not appear in the simplest examples of interacting Pock spaces): b y taking different test functions, the vacuum distribution of the field ope rator does not change only parametrically, but radically. In particular we nd the semi-circle, the reciprocal-semi-circle (or Arcsine), the double-bet a,..., and many other distributions.