  The instantonic approach for a $\phi^4$ 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 {\it 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 {\it infinite} size system.
This formal contradiction can be consistently overcome by the finite size
instantonic theory based on the Jacobi elliptic functions formalism. In terms
of the latter I derive in detail the classical background which solves the
finite size Euler-Lagrange equation and obtain the general path integral in
finite size. Both problem and solution offer an instructive example of fruitful
interaction between mathematics and physics.
  {\bf Keywords: Path Integral Methods, Finite Size Systems, Instantons}
