A Krein space based matter field theory is
provided. From the Mie theory the concept of discrete energy knots is taken
modelled by a physical problem specific (self-adjoint) kinetic energy operator.
From the correspondingly defined Krein space framework the concept of a (self-adjoint)
potential energy operator is applied. It enables the definition of potential energy norms on all of the Krein space
built on sets of quantum numbers leading to a (vacuum,
plasma, Mie) grouping of the concerned quantum elements.