Characterization of product states on polynomial algebras in terms of scalar products of $n$-particle vectors

The main goal of the algebraic approach to the theory of orthogonal polynomials is to construct explicit examples of interacting measures, as opposed to product measures, and to study the associated extensions of usual quantum theory (which can only cover product measures). In this (non-linear quantization) program, characterizations of product states on polynomial algebras play an important role because they indicate which properties of usual quantum theory cannot be expected to be realized in its non-linear extensions. One of these properties is known since a long time: commutativity of creators/annihilators corresponding to independent degrees of freedom. Another such property will be discussed in the present talk: orthogonality of $n$-particle vectors corresponding to different multi-indexes.

Организация лекции поддержана МЦМУ МИАН и грантом Фонда Саймонса.