Three different methods, viz., (i) a perturbative analysis of the Schrödinger equation, (ii) an abstract differential geometric method, and (iii) a semiclassical reduction of the Wheeler-Dewitt equation, relating the Pancharatnam phase to vacuum instability are discussed. An improved semiclassical reduction is also shown to yield the correct zeroth-order semiclassical Einstein equations with back reaction. This constitutes an extension of our earlier discussions on the topic.

• Received 6 July 1993

DOI:https://doi.org/10.1103/PhysRevD.48.5746