具有共形标量场的量子虫洞

QUANTUM WORMHOLE WITH CONFORMAL SCALAR FIELD

本文用Hartle-Hawking的方法讨论了具有共形标量场的量子虫洞,导出了相应的Wheeler-De Witt方程,计算了虫洞波函数,所得到的虫洞波函数是两个谐振子解的乘积。由虫洞波函数的分析,发现虫洞在α=0处出现几率密度为零,虫洞基态最可几半径为Planck尺度;由虫洞波函数的分析,还发现虫洞最有可能处在较小的φ值状态。

Using the Hartle-Hawking method, we discuss the quantum wormhole with conformal scalar field. The corresponding wheeler-De Witt equation was derived, and the wave function of the wormhole calculated. The wormhole's wave function we obtained is the product of double harmonic solutions. After analysing the wormhole's wave function, we found that the probability density of the wormhole equals appearing at a=0, and that the minimal radius of the graund state of the wormhole is on the planck scale. Analysing the wormhole's wave function also reveals that the wormhole was likely be piled at Φ=0.