Self-Adjointness criterion for operators in Fock spaces

Marco Falconi (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper we provide a criterion of essential self-adjointness for operators in the tensor product of a separable Hilbert space and a Fock space. The class of operators we consider may contain a self-adjoint part, a part that preserves the number of Fock space particles and a non-diagonal part that is at most quadratic with respect to the creation and annihilation operators. The hypotheses of the criterion are satisfied in several interesting applications.

Mots clés: Pauli-Fierz Hamiltonian; Interacting Quantum Field Theories; Fock Spaces; Essential Self-Adjointness

Domaines: Analyse fonctionnelle [math.FA]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Marco Falconi. Self-Adjointness criterion for operators in Fock spaces. Mathematical Physics, Analysis and Geometry, 2015, 18 (article 2), 18 p. ⟨10.1007/s11040-015-9173-x⟩. ⟨hal-00997074⟩