That is, we replace \[\int\!\!{d^d\!k\over (2\pi)^d}\>F(\Bk) \longrightarrow \int\!\!{d^d\!k\over (2\pi)^d}\>F(\Bk)\,\gla(\Bk)\ ,\] where \(F(\Bk)\) is any function and \(\gla(\Bk)\) is the cutoff fun...That is, we replace \[\int\!\!{d^d\!k\over (2\pi)^d}\>F(\Bk) \longrightarrow \int\!\!{d^d\!k\over (2\pi)^d}\>F(\Bk)\,\gla(\Bk)\ ,\] where \(F(\Bk)\) is any function and \(\gla(\Bk)\) is the cutoff function. The idea behind renormalization is that we can successively winnow degrees of freedom from a system in some exact or approximate way, and in so doing we generate a new version of the system, at a different length scale \(\ell'>\ell\), and with different couplings \(\{K'_\alpha\}\).
