Abstract
In this paper we consider the set of quantum states and passages to the limit for sequences of quantum dynamic semigroups in the mentioned set. We study the structure of the set of extreme points of the quantum state set and represent an arbitrary state as an integral over the set of one-dimensional orthogonal projectors; the obtained representation is similar to the spectral decomposition of a normal state. We apply the obtained results to the analysis of sequences of quantum dynamic semigroups which occur in the regularization of a degenerate Hamiltonian.
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