Because a field is incepted or operated under either virtual or physical primacy of an formula_7 or formula_8 manifold respectively and simultaneously, each point of the fields is entangled with and appears as a conjugate function of the scalar field formula_9 or formula_10 in its opponent manifold. A field can be classified as a scalar field, a vector field, or a tensor field according to whether the represented physical horizon is at a scope of scalar, vector, or tensor potentials, respectively.