The aim of this paper is to present the construction of a general family of C∗-algebras which includes, as a special case, the “quantum spacetime algebra” introduced by Doplicher, Fredenhagen, and Roberts. It is based on an extension of the notion of C∗-completion from algebras to bundles of algebras, compatible with the usual C∗-completion of the appropriate algebras of sections, combined with a novel definition for the algebra of the canonical commutation relations using Rieffel’s theory of strict deformation quantization. Taking the C∗-algebra of continuous sections vanishing at infinity, we arrive at a functor associating a C∗-algebra to any Poisson vector bundle and recover the original DFR-algebra as a particular example.
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Research Article| February 11 2016
C∗-completions and the DFR-algebra
Michael Forger, Daniel V. Paulino; C∗-completions and the DFR-algebra. J. Math. Phys. 1 February 2016; 57 (2): 023517. https://doi.org/10.1063/1.4940718
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