  There are several equivalent descriptions for constant B-field background of
open string. The background can be interpreted as constant B-field as well as
constant gauge field strength or infinitely many D-branes with non-commuting
Chan-Paton matrices. In this article, the equivalence of these open string
theories is studied in Witten's cubic open string field theory. Through the map
between these equivalent descriptions, both algebra of non-commutative
coordinates as well as Chan-Paton matrix algebra are identified with
subalgebras of open string field algebra.
