We solve the problem of constructing a genus-zero full conformal field theory
(a conformal field theory on genus-zero Riemann surfaces containing both chiral
and antichiral parts) from representations of a simple vertex operator algebra
satisfying certain natural finiteness and reductive conditions. We introduce a
notion of full field algebra which is essentially an algebraic formulation of
the notion of genus-zero full conformal field theory. For two vertex operator
algebras, their tensor product is naturally a full field algebra and we
introduce a notion of full field algebra over such a tensor product. We study
the structure of full field algebras over such a tensor product using modules
and intertwining operators for the two vertex operator algebras. For a simple
vertex operator algebra V satisfying certain natural finiteness and reductive
conditions needed for the Verlinde conjecture to hold, we construct a bilinear
form on the space of intertwining operators for V and prove the nondegeneracy
and other basic properties of this form. The proof of the nondegenracy of the
bilinear form depends not only on the theory of intertwining operator algebras
but also on the modular invariance for intertwining operator algebras through
the use of the results obtained in the proof of the Verlinde conjecture by the
first author. Using this nondegenerate bilinear form, we construct a full field
algebra over the tensor product of two copies of V and an invariant bilinear
form on this algebra.