  Expressions for generalized charge stiffness constant at zero temperature are
derived corresponding to low dimensional hole doped quantum antiferromagnets,
describable by the t-J-like models, with a view to understanding fermionic
pairing possibilities and charge couplings in the itinerant antiferromagnetic
systems. A detailed comparison between spin and charge correlations and
couplings are presented in both strong and weak coupling limits. The result
highlights that the charge and spin couplings show very similar behaviour in
the over-doped region in both the dimensions, whereas they show a completely
different trend in the lower doping regimes. A qualitative equivalence of
generalized charge stiffness constant with the effective Drude weight and
Coulomb interaction is established based on the comparison with other
theoretical and experimental results. The fall in charge stiffness with
increase in doping then implies reduction in the magnitude of effective Coulomb
repulsion between the mobile carriers. This leads to an enhanced possibility of
fermionic pairing with increase in doping in the possible presence of some
other attraction producing mechanism from a source outside the t-J-like models.
Moreover, under certain conditions in the weakly correlated phase, the t-J-like
models themselves are able to produce attractive interaction for pairing.
