## ABSTRACT

In the case of decay rate problem, the potential barrier separates the potentialminimum from the continuum where the system is energetically allowed to go to inﬁnity [see Figure 1.1(b)]. The general formulation developed in Chapter 6 for tunneling splitting can be applied to the present problem with some modiﬁcations [44]. The instanton trajectoryq0(τ ) starts in the inﬁnitely remote past at τ = −∞ frompotentialminimum and returns back to the minimum in the inﬁnitely remote future at τ = ∞. This periodic orbit always goes through a turning point on the potential contour V (q) = 0, which can be assumed to occur at τ = 0.