  Here the Origin of the pseudogap in HTSC is attributed to the modulated
antiferromagnetic (AFM) phase, whose preliminary version has been sketched
recently by the present author [1](arXiv:0901.3896v2 (cond.-mat.sup-con)).
Starting from the t-J Hamiltonian, I show that the formal failure of the
perturbation theory leads to a transformation to the pseudogap phase. This
phase is characterized by the aggregation of the holes into rows and columns,
which in turn results in two internal fields. The first is the modulated AFM
field, whose main evidence comes from Neutron scattering experiments. The
second internal field is made up by the checkerboard charge density waves that
have been observed by Scanning Tunneling Measurements. The present paper deals
mainly with the internal field of the first type, and discusses the second type
only tentatively. Formalism is derived that yields the ground state, the
internal field, the Hamiltonian, and the propagators of the condensed phase.
Our results resolve the presumably inherent self contradictory concept of
pseudogap. It is shown that the excitation energy spectrum is gapless despite
the order parameter that is inherent to the condensed system. In addition, it
is shown qualitatively that our model predicts "Fermi surface" that is in
agreement with experiment.
