WAVE-PACKET IN QUANTUM COSMOLOGY AND DEFINITION OF SEMICLASSICAL TIME

We consider a quantum cosmology with a massless background scalar fiel d phi(B) and adopt a wave packet as the wave function. This wave packe t is a superposition of the WKB form wave functions, each of which has a definite momentum of the scalar field phi(B). In this model it is s hown that to trace the formalism of the WKB time is seriously difficul t without introducing a complex value for a time. We define a semiclas sical real time variable T-P from the phase of the wave packet and cal culate it explicitly. We find that, when a quantum matter held phi(Q) is coupled to the system, an approximate Schrodinger equation for phi( Q) holds with respect to T-P in a region where the size a of the unive rse is large and \phi(B)\ is small.