  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.
