We discuss the construction of wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in Robertson-Walker type cosmologies. We present an ansatz for the initial conditions which leads to a unique determination of the expansion coefficients in the construction of the wave packets with probability distributions which, in an interesting contrast to some of the earlier works, agree well with all possible classical paths. The possible relationship between these initial conditions and signature transition in the context of classical cosmology is also discussed.

In this paper we compute the Casimir energy for a coupled fermion-pseudoscalar field system. In the model considered in this paper the pseudoscalar field is static and prescribed with two adjustable parameters. These parameters determine the values of the field at infinity (±θ0) and its scale of variation (µ). One can build up a field configuration with arbitrary topological charge by changing θ0, and interpolate between the extreme adiabatic and non-adiabatic regimes by changing µ. This system is exactly solvable and therefore we compute the Casimir energy exactly and unambiguously by using an energy density subtraction scheme. We show that in general the Casimir energy goes to zero in the extreme adiabatic limit, and in the extreme non-adiabatic limit when the asymptotic values of the pseudoscalar field properly correspond to a configuration with an arbitrary topological charge. Moreover, in general the Casimir energy is always positive and on the average an increasing function of θ0 and always has local maxima when there is a zero mode, showing that these configurations are energetically unfavorable. We also compute and display the energy densities associated with the spectral deficiencies in both of the continua, and those of the bound states. We show that the energy densities associated with the distortion of the spectrum of the states with E > 0 and E < 0 are mirror images of each other. We also compute and display the Casimir energy density. Finally we compute the energy of a system consisting of a soliton and a valance electron and show that the Casimir energy of the system is comparable with the binding energy.

We discuss the construction of wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in Robertson-Walker type cosmologies, for arbitrary curvature. We show that there always exists a "canonical initial slope" for a given initial wave function, which optimizes some desirable properties of the resulting wave packet, most importantly good classical-quantum correspondence. This can be properly denoted as a canonical wave packet. We introduce a general method for finding these canonical initial slopes which is generalization of our earlier work.

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We calculate the next to the leading order Casimir effect for a real scalar field, within φ 4 theory, confined between two parallel plates in three spatial dimensions with the Dirichlet boundary condition. In this paper we introduce a systematic perturbation expansion in which the counterterms automatically turn out to be consistent with the boundary conditions. This will inevitably lead to nontrivial position dependence for physical quantities, as a manifestation of the breaking of the translational invariance. This is in contrast to the usual usage of the counterterms in problems with nontrivial boundary conditions, which are either completely derived from the free cases or at most supplemented with the addition of counterterms only at the boundaries. Our results for the massive and massless cases are different from those reported elsewhere. Secondly, and probably less importantly, we use a supplementary renormalization procedure, which makes the usage of any analytic continuation techniques unnecessary.