Since there are indications (from string theory and concrete models) that one must consider relativistic quantum field theories with a fundamental length the question of a suitable framework for such theories arises. It is immediately evident that quantum field theory in terms of tempered distributions and even in terms of Fourier hyperfunctions cannot meet the (physical) requirements. We argue that quantum field theory in terms of ultra-hyperfunctions is a suitable framework. For this we propose a set of axioms for the fields and for the sequence of vacuum expectation values of the fields, prove their equivalence, and we give a class of models (analytic, but not entire functions of free fields).

No abstract

This article gives a brief overview of some recent progress in the characterization and parametrization of density matrices of finite dimensional systems. We discuss in some detail the Bloch-vector and Jarlskog parametrizations and mention briefly the coset parametrization. As applications of the Bloch parametrization we discuss the trace invariants for the case of time dependent Hamiltonians and in some detail the dynamics of three-level systems. Furthermore, the Bloch vector of two-qubit systems as well as the use of the polarization operator basis is indicated. As the main application of the Jarlskog parametrization we construct density matrices for composite systems. In addition, some recent related articles are mentioned without further discussion.

No abstract

No abstract