PREFERRED BASIS IN QUANTUM-THEORY AND THE PROBLEM OF CLASSICALIZATIONOF THE QUANTUM UNIVERSE

We revive an old proposal of Zeh for the preferred basis in the many-w orlds interpretation of quantum mechanics. The algorithm for the basis reduces to the eigenvalue problems for density matrices of subsystems forming the whole system under consideration. We generalize this proc edure to the case of degenerate eigenvalues of reduced density matrice s. A semiclassical calculational method for these eigenvalues is devel oped and applied to some model problems. The classical properties of e lements of the preferred basis are investigated. It is shown that clas sicality exists only in some part of many-worlds branches. Moreover, i t depends crucially on the initial conditions and Hamiltonians and und er some circumstances turns out to be a temporary phenomenon. Applicat ions of the preferred-basis proposal to quantum cosmology are discusse d. The relation between the preferred-basis approach and quantum-histo ries approach is discussed.