The Hamiltonian Analysis for Yang-Mills Theory on $R\times S^2$

Details The Hamiltonian Analysis for Yang-Mills Theory on $R\times S^2$ The Hamiltonian Analysis for Yang-Mills Theory on $R\times S^2$

2008-07-14

arxiv.org/abs/0807.2131v1

Nucl.Phys.B816:117-138,2009

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1016/j.nuclphysb.2009.03.007

Pure Yang-Mills theory on ${\mathbb R} \times S^2$ is analyzed in a gauge-invariant Hamiltonian formalism. Using a suitable coordinatization for the sphere and a gauge-invariant matrix parametrization for the gauge potentials, we develop the Hamiltonian formalism in a manner that closely parallels previous analysis on ${\mathbb R}^3$. The volume measure on the physical configuration space of the gauge theory, the nonperturbative mass-gap and the leading term of the vacuum wave functional are discussed using a point-splitting regularization. All the results carry over smoothly to known results on ${\mathbb R}^3$ in the limit in which the sphere is de-compactified to a plane.

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