renormalization and divergences....

eljose

let suppose we have a formula for the mass in the form:

[tex]m=\int_{0}^{\infty}dxf(x)e^{-ax} [/tex] [tex]a=ln\epsilon [/tex]

with epsilon tending to zero so a is divergent..but if we perform the integral numerically:

[tex]m=\sum_{j}w(x_{j})c_{j}f(x_{j})e^{-ax_{j}) [/tex]

so we could express the quantity a in terms of the mass m so [tex]a=g(m)[/tex] so we could put inside the integral to calculate the m:

[tex]m=\int_{0}^{\infty}dxf(x)e^{-xg(m)} [/tex] and from this equation obtain a value for the mass m.

I Know something similar is made for renormalizable theory..but why can not be made for non-renormalizable ones?...