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Can Quantum Wormholes really help set Λ → 0 ?

We ﬁnd the quantum analogues of wormholes obtained by Carlini and Miji´c (CM), who analytically continued closed universe models. The CM requirement that the strong energy condition ( γ > 2 / 3) be satisﬁed is shown to be consistent with the Hawking-Page conjecture for quantum wormholes as solutions of the Wheeler-DeWitt equation. The presence of a cosmological constant Λ violates such a condition and so prevents wormholes occurring. It is therefore inconsistent to invoke these wormholes to make Λ a dynamical variable: used in ar-guments which suggest Λ → 0. We analyse instead a simple model with just Λ present. Diﬀering results are obtained depending on the boundary conditions applied. In the Euclidean regime only the Hartle-Hawking boundary condition gives the factor exp (1 / Λ) but is badly behaved for negative Λ . Tunneling boundary conditions suggest an initially large value for Λ. Whereas in the Lorentzian region all boundary conditions suggest an initially large value of Λ for spatial curvature k = 1. This diﬀers from the previously obtained result of Strominger[28] for such models.