2012/01/07 by Michael Forger, Forger, Michael, Daniel V. Paulino +1
Mathematics · Physics and Astronomy · #46L08 #46L65 #53D55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1201.1583
openalex publication_date 2012/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of the present paper is to present the construction of a general family of C^*-algebras that includes, as a special case, the "quantum space-time algebra" first introduced by Doplicher, Fredenhagen and Roberts. To this end, we first review, within the C^*-algebra context, the Weyl-Moyal quantization procedure on a fixed Poisson vector space (a vector space equipped with a given bivector, which may be degenerate). We then show how to extend this construction to a Poisson vector bundle over a general manifold M, giving rise to a C^*-algebra which is also a module over C0(M). Apart from including the original DFR-model, this method yields a "fiberwise quantization" of general Poisson manifolds.