Quantum Cosmology. I

摘要: The Hamiltonian methods of Arnowitt, Deser, and Misner can be applied to homogeneous cosmological models, prove an efficient way both constructing the Einstein equations studying their solutions. By using appropriate form for metric, one finds that constraint these models solved explicitly, resulting problem in mechanics resembles a particle potential well. most unusual feature is it explicitly time dependent. There easy attractive choice factor orderings which allows pass on quantum theory (by imposing canonical commutation relations independent variables) while maintaining signature quantized metric. For closed-space model (Bianchi type IX) studied detail, classical (high-quantum-number) state remains as wave function followed back toward initial singularity. no tendency significant contributions from states low number develop even when radius universe much less than ${(\frac{G\ensuremath{\hbar}}{{c}^{3}})}^{\frac{1}{2}}={10}^{\ensuremath{-}33}$ cm.