1997/10/09 by Bogdan Morariu
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Feynman diagram #Lie algebra #Lie group #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Path integral formulation #Phase space #Physics #Poisson bracket #Poisson manifold #Pure mathematics #Quantization (signal processing) #Quantum #Quantum mechanics #Special unitary group #Symplectic geometry #Symplectic group #Unitary state #hep-th #math-ph #math.MP #math.QA
paper · pdf · doi:10.1142/s0217751x99000452
published as Int.J.Mod.Phys.A14:919-936,1999 · 24 pages, LaTeX, no figures, full postscript available from http://phyweb.lbl.gov/theorygroup/papers/40890.ps
arxiv created 1997/10/09 · openalex publication_date 1999/03/10 · arxiv updated 2014/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Feynman path integral is used to quantize the symplectic leaves of the Poisson–Lie group SU(2)*. In this way we obtain the unitary representations of [Formula: see text]. This is achieved by finding explicit Darboux coordinates and then using a phase space path integral. I discuss the *-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. I also compare the results with the path integral quantization of spin.