The concept of “nonlocalization” associated with the gravitational field, which is carried by the internal variable (θ) annexed to each point, is considered in connection with the geometrical theory of gauge fields. Two concrete examples of “nonlocalization” are proposed by taking θ as a vector and a spinor, respectively.

Under the assumption that the so-called space-time fluctuationy(x) in a classical sense, attached to each point of the gravitational field at some microscopic stage, is summarized as the metrical fluctuation in the formg λκ (x)=gλκ (x)·exp2σ(y(x)), some new physical aspects induced by the conformal scalarσ(x) (≡σ(y(x))) are found: By introducing the torsionT κ λμ (x) from a general standpoint, the resulting micro-gravitational field is made to have a conformally non-Riemannian structure, where a special form ofT κ λμ (i.e.,T κ λμ (...) =δ κ λ σμ−δ κ μ σλ(σμ=∂σ/∂x μ)) shows some peculiar features. An averaging process with respect toy is taken into account, by which the spatial structure of the corresponding macro-field is shown, in general, to have a somewhat “non”-Riemannian structure due to the contributions of the torsionT κ λμ. (shrink)