  In this work we take view on space-time as dual representation of fields on
manifold. Given we accept such view, the space of functions in operator
representation becomes probability amplitudes f(x) of a particle. Since the
probabilistic interpretation of f(x) module follows from f(x) and f*(x)
duality, the problem of finding representation of wave function reduces to
Frobenius theorem for division algebras. We then construct the gravity model
and the model of strong interactions as a logical implication of the extension
of fields interaction algebra to non-associative algebra of octonions. The
application of Penrouse approach in spinor representation of space-time
combined with the proposed approach further leads us to chirality of
interactions and absence of right neutrino and left spinors in singleton state.
We also show the obtained model is consistent with general theory of relativity
and SU(3) for distances larger than Planck length. The obtained model also
contains the generalization of general theory of relativity to the model with
torsion given the chirality of the field. Importantly, the application of our
approach gives us Einstein equation with gravity constant equal to squared
Planck mass as consequence of non-associativity of interactions fields. We
construct strong interaction model based on matrix representation of octonion
algebra with special multiplication rule. The strong interaction is induced by
vector fields of octonion algebra with constant gravity force, which is in turn
induced by a pair of charged $W$ vector bosons from standard theory of weak
interactions. The problem of quark confinement is presented as a spinor
solution inside "black hole".
