Proper condensates and long range order

Within the framework of algebra canonical commutation relations in Euclidean space, a long range order between particles bounded regions is established states with sufficiently large particle number. It occurs whenever homogeneous proper (infinite) condensates form locally limit infinite densities. The are described by eigenstates momentum operator, covering also those cases, where they streaming constant velocity. arguments given model independent and lead to new criterion for occurrence condensates. makes use novel approach identification condensates, based on characterization regular singular wave functions.