  The bound state generating functional is constructed in gauge theories. This
construction is based on the Dirac Hamiltonian approach to gauge theories, the
Poincar\'e group classification of fields and their nonlocal bound states, and
the Markov-Yukawa constraint of irreducibility. The generating functional
contains additional anomalous creations of pseudoscalar bound states:
para-positronium in QED and mesons in QCD in the two gamma processes of the
type of \gamma + \gamma = \pi_0+para-positronium. The functional allows us to
establish physically clear and transparent relations between the perturbative
QCD to its nonperturbative low energy model by means of normal ordering and the
quark and gluon condensates. In the limit of small current quark masses, the
Gell-Mann-Oakes-Renner relation is derived from the Schwinger-Dyson (SD) and
Bethe-Salpeter (BS) equations. The constituent quark masses can be calculated
from a self-consistent non-linear equation.
