2009/09/30 by Ricardo José Rocha Amorim, Ricardo Amorim, Éverton M. C. Abreu +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Black Holes and Theoretical Physics #Formalism (music) #Hilbert space #Invariant (physics) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #Scalar (mathematics) #Scalar field #hep-th
paper · pdf · doi:10.1103/physrevd.80.105010
13 pages. Latex. Final version to appear in Physical Review D
arxiv created 2009/10/20 · openalex publication_date 2009/11/12 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this work we analyze complex scalar fields using a new framework where the object of noncommutativity \ensuremathθ^\ensuremathμ\ensuremathν represents independent degrees of freedom. In a first quantized formalism, \ensuremathθ^\ensuremathμ\ensuremathν and its canonical momentum \ensuremathπ_\ensuremathμ\ensuremathν 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 Poincar'e group of symmetry. In a second quantized formalism perspective, we present an explicit form for the extended Poincar'e 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.