The story of Van Vleck's and Morette Van Hove's determinants

The genesis of Pauli's formula dating from late 1949 or early 1950, for the semiclassical approximation to Feynman's propagator (which is identical to Dirac's transformation function of type (q\Q) introduced in 1933) and that of Van Vleck's, in 1928, for the second order approximation to Dirac's transformation function introduced in 1927, and which can be identified as being of type (q\P), are carefully reexamined. We show that the action integrals and generating functions which enter Pauli's and Van Vleck's formulae are of type commonly called 1 and 2, respectively, the same being of course true for their Jacobians. Convincing evidence is provided that the determinant which enters Pauli's formula is due to Morette and Van Hove and not to Van Vleck as usually referred to in the literature on this subject.