Instantonic methods for quantum tunneling in finite size

The instantonic approach for a Φ4 model potential is reexamined in the asymptotic limit. The path integral of the system is derived in semiclassical approximation expanding the action around the classical background. It is shown that the singularity in the path integral, arising from the zero mode in the quantum fluctuation spectrum, can be tackled only assuming a finite (although large) system size. On the other hand the standard instantonic method assumes the (anti)kink as classical background. But the (anti)kink is the solution of the Euler-Lagrange equation for the infinite size system. T...