  We consider the massless minimally coupled scalar field in the de Sitter
ambient space formalism as a gauge potential or connection field. We construct
the scalar gauge theory by helping an arbitrary constant five-vector field
$B^\alpha$ analogous to the standard gauge theory. The Lagrangian density of
the interaction between the scalar and spinor fields is presented in this
framework. The Yukawa potential can be extracted from this Lagrangian density
at the null curvature limit by an appropriate choice of a constant five-vector
field. It is shown that the de Sitter ambient space formalism permits us to
unify the scalar and vector gauge fields. By choosing a matrix form for the
constant five-vector field $B^\alpha$, the unification of scalar and vector
gauge fields in the spectral action of noncommutative geometry can be
rewritten. We discuss that if the scalar gauge field is considered as a
conformal sector of the background metric field, it may be interpreted as the
connection field between the different de Sitter hyperboloids in the quantum
geometry from the classical point of view.
