Ginzburg-Landau Approach toL≠0Pairing

By comparing the predictions of the weak-coupling BCS theory with a general Ginzburg-Landau approach, we show that the weak-coupling model may give a qualitatively incorrect description of pairing with $L\ne 0$. Specific examples of the errors the weak-coupling model leads to are described for $d$- and $p$-wave pairing. In the latter case the general Ginzburg-Landau approach has structure enough to account for the current discrepancies between the weak-coupling predictions and the observed behavior of the low-temperature transition in liquid ${\mathrm{He}}_3$.