COMPLEX LAPSE, COMPLEX ACTION, AND PATH-INTEGRALS

Imaginary time is often used in quantum tunneling calculations. This a rticle advocates a conceptually sounder alternative: complex lapse. In the ''3+1'' action for the Einstein gravitational field minimally cou pled to a klein-Gordon held, allowing the lapse function to be complex yields a complex action that generates both the usual Lorentzian theo ry and its Riemannian analogue and in particular allows a change of si gnature between the two. The action and variational equations are mani festly well defined in the Hamiltonian representation, with the moment um fields consequently being complex. The complex action interpolates between the Lorentzian and Riemannian actions as they appear formally in the respective path integrals. Thus the complex-lapse theory provid es a unified basis for a path-integral quantum theory of gravity invol ving both Lorentzian and Riemannian aspects. A major motivation is the quantum-tunneling scenario for the origin of the universe. Taken as a n explanation for the observed quantum tunneling of particles, the com plex-lapse theory determines that the argument of the lapse for the un iverse now is extremely small but negative.