Quark-confinement mechanism for SU(2) Yang-Mills theory in abelian gauge

Kou Su-Peng

doi:doi:10.1007/s100520100557

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2022 Impact factor 4.4

Particles and Fields

Eur. Phys. J. C 19, 113-127
DOI: 10.1007/s100520100557

Quark-confinement mechanism for SU(2) Yang-Mills theory in abelian gauge

Kou Su-Peng

Center for Advanced Study, Tsinghua University, Beijing, 100084, P.R. China

(Received: 4 September 2000 / Published online: 23 February 2001 -© Springer-Verlag 2001)

Abstract
By dimensional reduction in the sense of Parisi and Sourlas (PS), the gauge fixing term in the abelian gauge of the SU(2) Yang-Mills field is reduced to a two-dimensional O(3) nonlinear $\sigma$ model. The confinement potential is obtained from magnetic monopoles and frame fluctuations. But the source of quark confinement is frame fluctuations and not magnetic monopoles. Because the frame T^a cannot be regarded as a fixed one, the abelian projected SU(2) Yang-Mills field turns into a ${\mathrm {U(1)}} \times {\mathrm {U(1)}}$ gauge field -one group element being $\exp (\mathrm i\varphi ^3T^3)$ with fixed frame T³, another group gauging the frame T³. The nonperturbative part $\varpi _\mu \left(x\right)$ becomes a dynamical gauge field in two dimensions, giving rise to the short range linear potential.