Derivations of a noncommutative algebra can be used to construct differential
calculi, the so-called derivation-based differential calculi. We apply this
framework to a version of the Moyal algebra M. We show that the
differential calculus, generated by the maximal subalgebra of the derivation
algebra of M that can be related to infinitesimal symplectomorphisms,
gives rise to a natural construction of Yang-Mills-Higgs models on M
and a natural interpretation of the covariant coordinates as Higgs fields. We
also compare in detail the main mathematical properties characterizing the
present situation to those specific of two other noncommutative geometries,
namely the finite dimensional matrix algebra Mn​(C) and the
algebra of matrix valued functions C∞(M)⊗Mn​(C). The
UV/IR mixing problem of the resulting Yang-Mills-Higgs models is also
discussed.Comment: 23 pages, 2 figures. Improved and enlarged version. Some references
have been added and updated. Two subsections and a discussion on the
appearence of Higgs fiels in noncommutative gauge theories have been adde