I'm trying to understand the method of calculating the transition probability of one vacuum state to another in a double well potential, using instantons. The reference I am following is Sidney Coleman's book "Aspects of symmetry".
The approach uses the path integral formulation of QM and we look at the semi-classical limit of small $\hbar$. In this limit our path integral is dominated by the stationary points of the (euclidean) action. Solving the equation of motion I find an infinite number of single instanton solutions (each different by a shift of the time origin of the instanton) starting at one vacuum and ending at the other.
For example, if I took a potential of the form
$V = \lambda(x^2-a^2)^2~~~$ and define $~~~\omega^2 = 8\lambda a^2$
our solution to the E.O.M with $~x(-\infty) = -a~$ and $~x(\infty) = a~$ would be
$x(t) = a\tanh\left(\frac{\omega}{2}(t-t_c)\right)$
where $t_c$, the center of the instanton is arbitrary.
Coleman then introduces other "approximate stationary points" which are effectively instanton/antiinstanton chains which start at one vacuum and end at the other. Coleman then continues in his analysis by adding up all of these approximate stationary point contributions to the original single instanton stationary point term.
My question is the following: in what sense are these multiple instanton/antiinstanton solutions "approximate stationary points"? (Is there some limit I can take where it becomes exact, or could someone explain why these paths don't have a negligible contribution to the path integral unlike other paths?)