Symmetries in the projection evolution model

Some introductory results concerning symmetries and conservation laws within the Projection Evolution (PEv) formalism are presented. It is shown that the PEv formalism conserves the quantum probability distributions after unitary transformations of the evolution operators represented by the orthogonal resolution of unity. Some conditions for transformations selecting the states with equal transition probabilities are found. A relation between a given symmetry represented by a Lie group and PEv conservation of the eigenvalues of the Casimir operator is derived. (paper)