FK-DLR states of a quantum bose-gas with a card-core interaction

Abstract: The paper focuses on infinite-volume bosonic states for a quantum particle system (a quantum gas) in a Euclidean space. The kinetic energy part of the Hamiltonian is the standard Laplacian (with a Dirichlet's boundary condition at the border of a `box'). The particles interact with each other through a two-body finite-range potential depending on the distance between them and featuring a hard core of a positive diameter. We introduce a class of so-called FK-DLR functionals containing all limiting Gibbs states of the system. In the next paper we will prove that any FK-DLR functional is shift-invariant, regardless of whether it is unique or not.