2010/11/15 by Amitabha Lahiri, Lahiri, Amitabha, Tae-Hun Lee +1
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1011.3428
28 pages, no figure
openalex publication_date 2010/11/15 · arxiv created 2011/05/24 · arxiv updated 2011/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the action for a non-Abelian charged particle in a non-Abelian background field in the worldline formalism, described by real bosonic variables, leading to the well known equations given by Wong. The isospin parts in the action can be viewed as the Lagrange multiplier term corresponding to a non-holonomic constraint restricting the isospins to be parallel transported. The path integration is performed over the isospin variables and as a result, the worldlines turn out to be constrained by the classical solutions for the isospins. We derive a wave equation from the path integral, constructed as the constrained Hamiltonian operator acting on the wave function. The operator ordering corresponding to the quantum Hamiltonian is found and verified by the inverse Weyl transformation.