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arXiv · 0909.0465

Quantum complex scalar fields and noncommutativity

Ricardo Amorim·Everton M. C. Abreu
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Abstract

In this work we analyze complex scalar fields using a new framework where the object of noncommutativity $θ^{μν}$ represents independent degrees of freedom. In a first quantized formalism, $θ^{μν}$ and its canonical momentum $π_{μν}$ 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.

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Ricardo Amorim, Everton M. C. Abreu. 2009-10-20. Quantum complex scalar fields and noncommutativity. https://doi.org/10.1103/physrevd.80.105010

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