Self-Adjointness criterion for operators in Fock spaces

TL;DR

This paper establishes a criterion for essential self-adjointness of certain operators in tensor products of Hilbert and Fock spaces, with applications to operators involving creation and annihilation operators.

Contribution

It introduces a new self-adjointness criterion applicable to operators with complex structures in Fock space tensor products.

Findings

Provides a self-adjointness criterion for operators in Fock spaces

Applicable to operators with creation and annihilation components

Validates the criterion in several interesting cases

Abstract

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.