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.