An approach to Unified Field Theory (UFT) is developed as a way to establish
quantum field theory (QFT) on background of covariant differential calculus.
A dual object, couple of spinor-like fields consisting of a covariant and
contra-variant function (dual s-field, DSF) is considered to represent matter
in a real n-dimensional unified manifold (UM). As a proposition in context of
interpretation, the manifold unifies space-time coordinates and non-gauge
fields of QFT as an aggregate of independent variables. DSF is considered a
primary fundamental object of UM based on isomorphism and irreducibility
principles. Based on extreme action principle, system of covariant differential
equations for DSF, affine s-tensor (connection object, AST) and dual couple
of triadic s-tensors, split metric is derived. Riemann-Christoffel curvature
form (RCF) is recognized as covariant derivative of affine s-tensor. Scalar
Lagrangian form is composed based on principles of irreducibility and conformal
invariance. It consists of a matter part and geometry part. Matter scalar is
structured as binary form on DSF and its covariant derivatives, drawing the
split metric. Geometry scalar is structured as bundle of non-simplified RCF
with an s-tensor form built as binary form on the split metric. Metric tensor
is inquired for invariant integration of scalar forms. It is composed as binary
bundle of the split metric. Type of manifold geometry is not chosen in
advance, neither in local (dimensionality, signature) or regional (topology)
aspects. No fundamental constants are introduced. Euler-Lagrange equations for
DSF are considered to play role of Schrödinger-Dirac equation of UM. Principles
of establishing the UM dimensionality, correspondence to QFT and General
Relativity, and aspects of possible asymptotic deductions of the model to
these theories will be discussed.