one loop result [@sch:prd] of $ Im\,L_{eff}^{(1)}$ term by term and observe that the particle production occurs due to the instability in the Hartle-Hawking vacuum. This lends support to keep the denominator in (30) which some authors (see concluding discussion) feel not necessary in the evaluation of the path integral.

To apply this approach in our case, we need a time contained description that will render a physical interpretation of $(1-exp(2i\,S))^{-1} $ term. Our approach is to treat the gravity as classical and retaining for $\phi$ the quantum behaviour and to obtain an quantum equation that contains the time.

**[Schroedinger-Wheeler-DeWitt Equation]{}**
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In our approach we keep only the $\delta\,S\equiv S_1$ term and consider the region in which $\nu\,a_f\gg 1$ and the gravity field could be treated classically such that $S_1<< S_0$ in the region of interest. By this we allow $a$ to be complex and is given by (19). We now eliminate $S_1$ through the following steps. In the region $\nu a_f>>1$ we take (see (11)) $${\partial \over {\partial t}}=-{1\over {Ma}}{{\partial S_o}\over {\partial a}} 
{{\partial}\over {\partial a}}\,.$$ At present we omit the subscript $0$ in $a_0$ and will be introduced when required. Equation (31) now gives the prescription of 