  In this thesis we calculate the baryon axial current within the combined
framework of the $1/N_c$ expansion and chiral perturbation theory, where $N_c$
is the number of colors. This calculation shall consider Feynman diagrams to
order of one-loop, octet and decuplet intermediaries states. We obtain
corrections due to one-loop and perturbative SU(3) symmetry breaking. The first
corrections come from Feynman diagrams, then talk about a broken chiral
symmetry in the implicit limit $m_q \rightarrow 0$, where $m_q$ is the quark
mass and the second corrections are obtained by ignoring isospin breaking and
in that case the SU(3) symmetry breaking a first-order perturbation is
included, leading an explicit break symmetry. The matrix elements of the
spatial components of the axial operator between the states of the spin flavor
symmetry, give the typical values of the axial vector coupling. For the baryon
octet, links axial vector are $g_A$, just as they are defined in experiments of
baryon semileptonic decays, where $g_A \approx 1.27$ for neutron beta decay. In
strong decays of the baryon axial vector couplings are $g$, which are extracted
from the widths of the strong decays of baryon decuplet to octet of baryons and
pions. The calculation of this work allows us to make various settings by
minimum squares, i.e., adjusting our analytical expressions with data pilot can
make the comparison between theory and experiment. We found the comparison of
our theoretical results with the experiment are in total agreement.
