2011/12/31 by Brian C. Hall, Jeffrey J. Mitchell · 1 citation
Mathematics · Physics and Astronomy · #Coherent states #Creation and annihilation operators #Eigenvalues and eigenvectors #Field (mathematics) #Mathematical physics #Mathematics #Phase space #Physics #Pure mathematics #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #Quantum mechanics #Quantum optics and atomic interactions #Theoretical physics #hep-th #math-ph #math.MP #msc:81Q35 #msc:81R30 #msc:81S30
paper · pdf · doi:10.1088/1751-8113/45/24/244025
published as Journal of Physics A: Mathematical and Theoretical 45 (2012) 244025 (18 pages) · 23 pages. To appear in Journal of Physics A, Special Issue on Coherent States
arxiv created 2012/01/19 · openalex publication_date 2012/05/30 · arxiv updated 2015/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We consider a particle moving on a 2-sphere in the presence of a constant magnetic field. Building on our earlier work in the nonmagnetic case we construct coherent states for this system. The coherent states are labeled by points in the associated phase space, the (co)tangent bundle of S 2 . They are constructed as eigenvectors for certain annihilation operators and expressed in terms of a certain heat kernel. These coherent states are not of Perelomov type but rather are constructed according to the ‘complexifier’ approach of Thiemann. We describe the Segal–Bargmann representation associated with the coherent states which is equivalent to a resolution of the identity. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.