A differential geometrical consideration on a “nonlocal” field

In this paper, the concept of “nonlocality”, which is carried by the internal variable (ω) ascribed to each point (x), is first investigated generally in connection with the concept of “unified” gauge field. Next, as a typical example, a Finslerian “nonlocal” field is considered, which is obtained by taking for ω a vector (ξ), and two examples are proposed: one is a unified field with Randers metric and the other is a micro-gravitational field endowed with space-time fluctuation.