Kontsevich's Universal Formula for Deformation Quantization and the Campbell-Baker-Hausdorff Formula, I

1998/11/30 by Vinay Kathotia, Kathotia, Vinay · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA

paper · pdf · doi:10.48550/arxiv.math/9811174

48 pages, over 90 (small) epsf figures, uses some ams-latex packages

openalex publication_date 1998/11/30 · arxiv created 1998/12/01 · arxiv updated 2009/11/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We relate a universal formula for the deformation quantization of arbitrary Poisson structures proposed by Maxim Kontsevich to the Campbell-Baker-Hausdorff formula. Our basic thesis is that exponentiating a suitable deformation of the Poisson structure provides a prototype for such universal formulae.

Citations

• The Principles of Quantum Mechanics
• Quantum mechanics as a statistical theory

Cited by

• Effective field theories on noncommutative space-time

Related

• On the Kontsevich and the Campbell-Baker-Hausdorff deformation quantizations of a linear Poisson structure
• Kontsevich's deformation quantization: from Dirac to multiple zeta values
• Lectures on Deformation quantization of Poisson manifolds
• Quantization of Poisson families and of twisted Poisson structures
• Deformation Quantisation via Kontsevich Formality Theorem