We point out that a field phi charged under a global U(1) symmetry generally allows for a starred localized extension with the transformation rule, phi --> U-L * phi * U-R(-1). This results in a double gauging of the global U(1) symmetry on noncommutative space. We interpret the gauge theory so obtained in terms of the gauge fields that in the commutative limit appear naturally and are respectively the gauge field responsible for the charge and a decoupled vector field. The interactions are shown to be very different from those obtained by assigning a transformation rule of phi --> U * phi or phi * U-1. (C) 2004 Elsevier B.V. All rights reserved.
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