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We propose a new systematic fibre bundle formulation of nonrelativisticquantum mechanics. The new form of the theory is equivalent to the usual onebut it is in harmony with the modern trends in theoretical physics andpotentially admits new generalizations in different directions. In it a purestate of some quantum system is described by a state section (along paths) of a(Hilbert) fibre bundle. It's evolution is determined through the bundle(analogue of the) Schr\"odinger equation. Now the dynamical variables and thedensity operator are described via bundle morphisms (along paths). Thementioned quantities are connected by a number of relations derived in thiswork.  The present fourth part of this series is devoted mainly to the fibre bundledescription of mixed quantum states. We show that to the conventional densityoperator there corresponds a unique density morphism (along paths) for whichthe corresponding equations of motion are derived. It is also investigated thebundle description of mixed quantum states in the different pictures of motion.We calculate the curvature of the evolution transport and prove that it iscurvature free iff the values of the Hamiltonian operator at different momentscommute.

FIBRE BUNDLE FORMULATION OF NONRELATIVISTIC QUANTUM MECHANICS IV: MIXED STATES AND EVOLUTION TRANSPORT'S CURVATURE