Periodicity, type $I{I}_1$ factors and free Poisson laws in interacting Fock spaces

Vitonofrio Crismale, Yun Gang Lu, Éric Ricard

We show that the von Neumann algebra generated by position operators in a 2-periodic interacting Fock space is a type $I{I}_1$ factor. On the probabilistic side, we prove that the sq…