  In this paper we introduce an alternative renormalization program for systems
with non-perturbative conditions. The non-perturbative conditions that we
concentrate on in this paper are confined to be either the presence of
non-trivial boundary conditions or non-perturbative background fields. We show
that these non-perturbative conditions have profound effects on all physical
properties of the system and our renormalization program is consistent with
these conditions. We formulate the general renormalization program in the
configuration space. The differences between the free space renormalization
program and ours manifest themselves in the counter-terms as well, which we
shall elucidate. The general expressions that we obtain for the counter-terms
reduce to the standard results in the free space cases. We show that the
differences between these divergent counter-terms are extremely small. Moreover
we argue that the position dependences induced on the parameters of the
renormalized Lagrangian via the loop corrections, however small, are direct and
natural consequences of the non-perturbative position dependent conditions
imposed on the system.
