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Self-Adjointness criterion for operators in Fock spaces

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.

preprint2015arXivOpen access
Marco Falconi
math-phmath.FAmath.MP
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Marco Falconi

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