Hilbert space description of classical dynamical systems II

K. Kowalski

K. Kowalski

Luigi Accardi

E. Deotto, E. Gozzi, D. Mauro

In this paper we analyze two different functional formulations of classical mechanics. In the first one the Jacobi fields are represented by bosonic variables and belong to the vector (or its dual) representation of the symplectic group. In the second formulation the Jacobi fields are given as condensates of Grassmannian variables belonging to the spinor representation of the metaplectic group. For both formulations we shall show that, differently from what happens in the case presented in paper I, it is possible to endow the associated Hilbert space with a positive definite scalar product and to describe the dynamics via a Hermitian Hamiltonian. The drawback of this formulation is that higher forms do not appear automatically and that the description of chaotic systems may need a further extension of the Hilbert space.

S. Wickramasekara

We construct two rigged Hilbert spaces that furnish differentiable representations of the causal Poincaré semigroup. These rigged Hilbert spaces provide the mathematical foundation for a theory of relativistic quasistable states that synthesizes the S-matrix description of resonance scattering with the Bakamjian–Thomas construction for interacting relativistic quantum systems.

Roberto Beneduci, James A. Brooke, Ray Curran +1 more