Quantum complex scalar fields and noncommutativity

Abstract

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 (DFR) algebra and is invariant under an extended Poincaré group of symmetry. In a second quantized formalism perspective, we present an explicit form for the extended Poincaré 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.

13 pages. Latex. Final version to appear in Physical Review D

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• The Noncommutative Doplicher-Fredenhagen-Roberts-Amorim Space
• Higgs Couplings in NonCommutative Standard Model
• Maximal acceleration in a Lorentz invariant non-commutative space-time
• From Noncommutative Sphere to Nonrelativistic Spin
• Casimir effect in DFR space-time
• The Strong Interaction Model in DFR noncommutative space-time
• Noncommutativity and Duality through the Symplectic Embedding Formalism
• Quantisation of Lorentz invariant scalar field theory in non-commutative space-time and its consequence
• N=2 supersymmetric radiation damping problem on a noncommutative plane