2010/11/15 by T. Koikawa, Koikawa, Takao
Mathematics · #Advanced Topics in Algebra #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1011.3289
openalex publication_date 2010/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We apply the star product quantization to the Lie algebra. The quantization in terms of the star product is well known and the commutation relation in this case is called the θ-deformation where the constant θ appears as a parameter. In the application to the Lie algebra, we need to change the parameter θ to x-dependent θ(x). There is no essential difference between the quantization in the quantum mechanics and deriving quantum numbers in the Lie algebra from the viewpoint of the star product. We propose to unify them in higher dimensions, which may be analogous to the Kaluza-Klein theory in the classical theory.