We show that the recently proposed doped carrier Hamiltonian formulation of
the t-J model should be complemented with the constraint that projects out the
unphysical states. With this new important ingredient, the previously used and
seemingly different spin-fermion representations of the t-J model are shown to
be gauge related to each other. This new constraint can be treated in a
controlled way close to half-filling suggesting that the doped carrier
representation provides an appropriate theoretical framework to address the t-J
model in this region. This constraint also suggests that the t-J model can be
mapped onto a Kondo-Heisenberg lattice model. Such a mapping highlights
important physical similarities between the quasi two-dimensional heavy
fermions and the high-Tc​ superconductors. Finally we discuss the physical
implications of our model representation relating in particular the small
versus large Fermi surface crossover to the closure of the lattice spin gap.Comment: corrected and enlarged versio