On unconstrained SU(2) gluodynamics with theta angle

Khvedelidze, A.; Mladenov, D. M.; Pavel, Hans-Peter; Röpke, G.

doi:10.1007/s100520200913

Cited by 2 publications

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“…It is the same functional of the symmetric field S as the original B ai (A), since the chromomagnetic field transforms homogeneously under the change of coordinates (14). Finally, the potential V (S) is the square of the reduced magnetic field (28),…”

Section: Hamiltonian Reduction For Arbitrary θ Anglementioning

confidence: 99%

“…Having this in mind, in the present paper we extend our approach [22,27,28], to constructing the unconstrained form of SU(2) Yang-Mills theory to the case when the topological term is included in the classical action. We generalize the Hamiltonian reduction of classical SU(2) Yang-Mills field theory to arbitrary θ angle by reformulating the original degenerate Yang-Mills theory as a nonlocal theory of a self-interacting positive definite symmetric 3 × 3 matrix field.…”

Section: Introductionmentioning

confidence: 99%

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UnconstrainedSU(2)Yang-Mills theory with a topological term in the long-wavelength approximation

et al. 2003

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The Hamiltonian reduction of SU(2) Yang-Mills theory for an arbitrary angle to an unconstrained nonlocal theory of a self-interacting positive definite symmetric 3ϫ3 matrix field S(x) is performed. It is shown that, after exact projection to a reduced phase space, the density of the Pontryagin index remains a pure divergence, proving the independence of the unconstrained theory obtained. An expansion of the nonlocal kinetic part of the Hamiltonian in powers of the inverse coupling constant and truncation to lowest order, however, lead to violation of the independence of the theory. In order to maintain this property on the level of the local approximate theory, a modified expansion in the inverse coupling constant is suggested, which for a vanishing angle coincides with the original expansion. The corresponding approximate Lagrangian up to second order in derivatives is obtained, and the explicit form of the unconstrained analogue of the Chern-Simons current linear in derivatives is given. Finally, for the case of degenerate field configurations S(x) with rankʈSʈϭ1, a nonlinear -type model is obtained, with the Pontryagin topological term reducing to the Hopf invariant of the mapping from the three-sphere S 3 to the unit two-sphere S 2 in the Whitehead form.

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Section: Hamiltonian Reduction For Arbitrary θ Anglementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%