  We investigate the consequences of Fierz transformations acting upon the
contact interactions for nucleon fields occurring in relativistic point
coupling models in Hartree approximation, which yield the same models but in
Hartree-Fock approximation instead. We find for four-fermion interactions
occurring in two existing relativistic point coupling phenomenologies that
whereas in Hartree the isovector-scalar strength, corresponding to delta-meson
exchange, is unnaturally small, indicating a possible new symmetry, in
Hartree-Fock it is instead comparable to the isovector-vector strength
corresponding to rho-meson exchange, but the sum of the two isovector coupling
constants appears to be preserved in both approaches. Furthermore, in
Hartree-Fock approximation, both QCD-scaled isovector coupling constants are
natural (dimensionless and of order 1) whereas in Hartree approximation only
that of the isovector-vector channel is natural. This indicates that it is not
necessary to search for a new symmetry and, moreover, that the role of the
delta-meson should be reexamined.
