  This paper continues the work Y. Suhov, M. Kelbert. FK-DLR states of a
quantum bose-gas, arXiv:1304.0782 [math-ph], and focuses on infinite-volume
bosonic states for a quantum system (a quantum gas) in a plane. We work under
similar assumptions upon the form of local Hamiltonians and the type of the
(pair) interaction potential as in the reference above. The result of the paper
is that any infinite-volume FK-DLR functional corresponding to the Hamiltonians
is shift-invariant, regardless of whether this functional is unique or not.
