An inhomogeneous toy model of the quantum gravity with the explicitly evolvable observables

作者：Cherkas S L^*; Kalashnikov V L

来源：General Relativity and Gravitation, 2012, 44(12): 3081-3102.

DOI：10.1007/s10714-012-1441-5

• Quantum gravity
• String on curved background
• Wheeler-DeWitt equation

An inhomogeneous (1 1)-dimensional model of the quantum gravity is considered. It is found, that this model corresponds to a string propagating in some curved background space. The quantization scheme including the Wheeler-DeWitt equation and the %26quot;particle on a sphere%26quot; type of the gauge condition is suggested. In the quantization scheme considered, the %26quot;problem of time%26quot; is resolved by building of the quasi-Heisenberg operators acting in a space of solutions of the Wheeler-DeWitt equation, and the normalization of the wave function corresponds to the Klein-Gordon type. To analyze the physical consequences of the scheme, a (1 1)-dimensional background space is considered for which a classical solution is found and quantized. The obtained estimations show the way to solution of the cosmological constant problem for this model. Such a solution consists in compensation of the zero-point oscillations of the matter fields by the quantum oscillations of the scale factor. Along with such a compensation, a slow global evolution of a background exists that corresponds to an universe expansion.

• 出版日期2012-12