Perturbation series

A perturbation series expands a correlation function or scattering amplitude in powers of interaction couplings. In quantum field theory it is commonly asymptotic because diagram counts grow factorially and nonperturbative effects are invisible to every finite order.

Weak coupling means a suitably dimensionless interaction strength is small. In BCS theory, ${\nu }_{s}V\ll 1$ gives a gap exponentially small compared with the pairing-shell energy cutoff; the expansion parameter is not the dimensional quantity $V$ alone.