Quantum complex scalar fields and noncommutativity

Details Quantum complex scalar fields and noncommutativity Quantum complex scalar fields and noncommutativity

2009-09-02

arxiv.org/abs/0909.0465v2

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

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 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.

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