Abstract
In this paper we investigated the causality problem present in the recent published work about the Doplicher–Fredenhagen–Roberts–Amorim (DFRA) noncommutative framework which analyzed the complex scalar field. We described the noncommutative Klein–Gordon equation with a source term. Its solution was accomplished through the retarded, advanced and causal Green functions constructed in this noncommutative ten-dimensional DFRA space–time. We believe that this solution constitutes the first step in the elaboration of a quantum field theory using the DFRA formalism where the well known noncommutative parameter from now on is an ordinary coordinate of the system and therefore has a canonical conjugate momentum. We discussed the dimensional reduction of this noncommutative space–time (D = 10) in order to recover commutativity in D = 4 space–time, which is not the usual one in noncommutativity literature.
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