Abstract
In this dissertation I present a new formalism for computing the wavefunction of a multidimensional quantum tunneling system, including vacuum bubble nucleation in the absence of gravitational effects. The formalism is based on the matching of transverse energy eigenstates at neighboring points along the semiclassical tunneling path. For curving semiclassical paths the formalism illustrates a phenomenon we call “anti-banking”, in which transverse energy eigenstates are displaced in the direction of curvature from the path. The evolution of states transmitted through a potential barrier is described in an intuitive way. I also show a technique for obtaining mode functions in field theory that obey a global constraint, and solve the resulting equation numerically for a few modes in nucleation of a vacuum bubble in one spatial dimension. Some of them exhibit tachyonic behavior deep under the effective tunneling potential, which is interpreted as a sign of instability of the field configuration there.