The Hamiltonian Analysis for Yang-Mills Theory on RxS2

Agarwal, Abhishek; Nair, V. P.

doi:doi:10.1016/j.nuclphysb.2009.03.007

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The Hamiltonian Analysis for Yang-Mills Theory on RxS2

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Agarwal, Abhishek
Duality & Integrable Structures, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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npb816_117.pdf
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0807.2131v1.pdf
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Citation

Agarwal, A., & Nair, V. P. (2009). The Hamiltonian Analysis for Yang-Mills Theory on RxS2. Nuclear Physics B, 816, 117-138. doi:doi:10.1016/j.nuclphysb.2009.03.007.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-4582-1

Abstract

Pure Yang-Mills theory on RxS2 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.