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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)

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 Ta 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.

© Società Italiana di Fisica, Springer-Verlag 2001