Quantum complex scalar fields and noncommutativity

In this work we analyze complex scalar fields using a new framework where the object of noncommutativity theta(mu nu) represents independent degrees of freedom. In a first quantized formalism, theta(mu nu) and its canonical momentum pi(mu nu) are seen as operators living in some Hilbert space. This structure is compatible with the minimal canonical extension of the Doplicher-Fredenhagen-Roberts algebra and is invariant under an extended Poincareacute group of symmetry. In a second quantized formalism perspective, we present an explicit form for the extended Poincareacute generators and the same algebra is generated via generalized Heisenberg relations. We also introduce a source term and construct the general solution for the complex scalar fields using the Green's function technique.