On the mathematical structure of the B.C.S.-model. II

Walter E Thirring

Walter E Thirring

Walter E Thirring, Alfred Wehrl

M. Courbage

We study in the frame of the superspace of the Hilbert–Schmidt operators the contributions of some complex singularities of the analytic continuation of (Ψ(z)−z)−1 to the diagonal part of the solution of the Liouville–von Neumann equation. Under some conditions, the θ̄ operator of the pseudo-Markovian master equation can be explicitly constructed. It is necessary to specify the diagonal representation and the class of initial conditions having regularity properties. This Hilbertian structure does not allow the construction of a closed subspace which reduces the Liouville–von Neumann operator L, giving an exact irreversible subdynamics; more elaborated mathematical structures are therefore necessary. The above methods are illustrated in the case of the Lee model.

Gianfausto Dell’Antonio

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced

R. Dagtas, O. Bayrak

The purpose of this note is threefold: (i) to recall (with some points made more explicit) the mathematical Weyl algebra model formulation, given before, of the Staruszkiewicz theory of quantum Coulomb field; (ii) to add some new elements to the discussion of the representation of the Lorentz group within this model; (iii) to comment on some statements on the structure of the theory which appeared recently.