Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1996-06-05
Int.J.Mod.Phys. A12 (1997) 859-872
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
20 pages, latex, no figures
Scientific paper
10.1142/S0217751X97000657
We consider a quantum cosmology with a massless background scalar field $\pb$ and adopt a wave packet as the wave function. This wave packet is a superposition of the WKB form wave functions, each of which has a definite momentum of the scalar field $\pb$. In this model it is shown that to trace the formalism of the WKB time is seriously difficult without introducing a complex value for a time. We define a semiclassical real time variable $\tp$ from the phase of the wave packet and calculate it explicitly. We find that, when a quantum matter field $\pq$ is coupled to the system, an approximate Schr\"odinger equation for $\pq$ holds with respect to $\tp$ in a region where the size $a$ of the universe is large and $|\pb|$ is small.
Kitazoe Tetsuro
Ohkuwa Yoshiaki
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