Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-11-15
Physics
High Energy Physics
High Energy Physics - Theory
28 pages, no figure
Scientific paper
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.
Lahiri Amitabha
Lee Tae-Hun
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