Wave Packet in Quantum Cosmology and Definition of Semiclassical Time
نویسنده
چکیده
We consider a quantum cosmology with a massless background scalar field φB 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 φB. 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 φQ is coupled to the system, an approximate Schrödinger equation for φQ holds with respect to TP in a region where the size a of the universe is large and |φB| is small.
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