Canonical transformation for stiff matter models in quantum cosmology

In the present work we consider Friedmann-Robertson-Walker models in the presence of a stiff matter perfect fluid and a cosmological constant. We write the superhamiltonian of these models using the Schutz's variational formalism. We notice that the resulting superhamiltonians have terms that will lead to factor ordering ambiguities when they are written as operators. In order to remove these ambiguities, we introduce appropriate coordinate transformations and prove that these transformations are canonical using the symplectic method.Comment: Revtex4 Class, 3 pages, No Figure

Características físico-químicas de amostras de leite de tanque comunitário.

Neste trabalho objetivou-se avaliar a qualidade físico-química do leite cru obtido de 72 amostras provenientes de nove propriedades rurais situadas na região da Gameleira, no município de Sacramento, MG, assim como doze amostras do leite dessas propriedades contido em um tanque comunitário. Foram determinados os valores de acidez titulável, densidade, crioscopia, teor de gordura, extrato seco total e extrato seco desengordurado (BRASIL, 1981). Os resultados obtidos evidenciaram que, de dez (13,9%) amostras estavam em desacordo com pelo menos um dos requisitos físico-químicos constantes na Instrução Normativa nº 51. As doze amostras de leite de conjunto analisadas durante o experimento apresentaram-se de acordo com o proposto pela Instrução Normativa n° 51 para os requisitos físico-químicos. Tais achados permitiram concluir que o uso de tanque comunitário pode proporcionar a obtenção de leite com qualidade físico-química satisfatória. Physical and chemical characteristics of milk samples from community tanks. Abstract - This research evaluated the physical and chemical quality of 72 samples of crude milk from 9 farms in the Gameleira region, municipality of Sacramento, MG, Brazil, and 12 milk samples from the same farms collected from a community milk tank. Values for titratable acidity, density, cryoscopy, fat, total dry extract, defatted dry extract were determined (BRASIL, 1981). Results showed that 10 (13.9%) samples did not comply with at least one physical and chemical item required by Norm 51. The 12 milk samples from the community tank analyzed during the assay complied with Norm 51 for physical and chemical requirements. The use of community tank actually provides satisfactory quality milk with regard to its physical and chemical characteristics

A canonical transformation and the tunneling probability for the birth of an asymptotically DeSitter universe with dust

In the present work, we study the quantum cosmology description of closed Friedmann-Robertson-Walker models in the presence of a positive cosmological constant and a generic perfect fluid. We work in the Schutz's variational formalism. If one uses the scale factor and its canonically conjugated momentum as the phase space variables that describe the geometrical sector of these models, one obtains Wheeler-DeWitt equations with operator ordering ambiguities. In order to avoid those ambiguities and simplify the quantum treatment of the models, we introduce new phase space variables. We explicitly demonstrate that the transformation leading from the old set of variables to the new one is canonical. In order to show that the above canonical transformations simplify the quantum treatment of those models, we consider a particular model where the perfect fluid is dust. We solve the Wheeler-DeWitt equation numerically using the Crank-Nicholson scheme and determine the time evolution of the initial wave function. Finally, we compare the results for the present model with the ones for another model where the only difference is the presence of a radiative perfect fluid, instead of dust.Comment: Revtex4, 18 pages, 2 EPS figure

Reply to "Comment on 'Quantization of FRW spacetimes in the presence of a cosmological constant and radiation'"

The Comment by Amore {\it et al.} [gr-qc/0611029] contains a valid criticism of the numerical precision of the results reported in a recent paper of ours [Phys. Rev. D {\bf 73}, 044022 (2006)], as well as fresh ideas on how to characterize a quantum cosmological singularity. However, we argue that, contrary to what is suggested in the Comment, the quantum cosmological models we studied show hardly any sign of singular behavior.Comment: 4 pages, accepted by Physical Review