与共形不变标量场耦合的Robertson Walker几何的量子化

本文采用约束哈密顿体系的正则描述对与共形不变标量场耦合的Robertson—Walker宇宙量子化,得到了相应的Wheeler—Dewitt方程的精确解,并且证明了在这种情况下代表量子引力中算符次序模糊的参数P等于零。最后,我们还证明了宇宙标度因子的最小值为普朗克长度,从而避免了宇宙向奇点的塌缩。

QUANTIZATION OF ROBERTSON-WALKER GEOMETRY COUPLED TO A CONFORMALLY INVARIANT SCALAR FIELD

A Robertson-walker universe coupled to a conformally invariant scalar field is quantized following the canonical formalism for constrained Hamil tonian systems. The exact solution is found to corresponding wheeler-Dewitt equation. It is shown that in the case under discussion the parameter p is vanishing. The parameter p denotes some factor-ordering ambiguty in the Quantum Gravitational Theory. It is also shown that the extreme value of the scale factor of the universe is of the order of planck length.