经典时空的量子共形起伏效应

EFFECT OF QUANTUM CONFORMAL FLUCTUATION ON CLASSICAL SPACE—TIME

本文证明了时空的共形起伏场除了一个普朗克长度1,的因子外.等价于一种与时空有共形耦合的负能长程标量场.在这种量子共形起伏下,任何时空的本征时间和本征长度的最小极限分别为普朗克时间 t,和普朗克长度1_p.将量子共形起伏方法用于封闭的 R-W 宇宙模型,则导致宇宙空间量子化的结论,其基态宇宙标度因子的期待值和各个定态标度因子期待值之间的间隔都具有普朗克长度的数量级.

A Conformal fluctuation field of space—time is equivalent to a long-range,negative energe scalar field eonformally coupled to space-time except a Planck length factor.It is shown that under the quantum conformal fluctuation the expectation values of the proper time and the proper length in any space-time are bounded at Planck time t_p and Planck Length l_prespectively.Cosidering a closed R-W cosmological model with the approach of quantum conformal fluctuation we find a conclusion that space of the uni- verse is quantized,and the expectation value of the scale factor of the ground state and interval between the expectation values of the scale factors of various stationary states are of the order of Planek Length.