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Quark energy in a three-dimensional QCD model with a constant background field. (English. Russian original) Zbl 1046.81100

Mosc. Univ. Phys. Bull. 56, No. 4, 45-49 (2001); translation from Vestn. Mosk. Univ., Ser. III 2001, No. 4, 38-41 (2001).
Summary: In an \(SU(2)\) Yang-Mills field model with a topological mass \(\theta\) in the space with dimensionality \(d=2+1\) and with account for an external background field, the one-loop quark energy correction is calculated. As a background field, the exact constant solutions of the Yang-Mills field equations are chosen. It is shown that, at the quark mass \(m=\frac 14\theta\), the effective quark mass remains equal to zero even when the calculated one-loop vacuum correction is taken into account. This fact may be caused by a certain internal symmetry of the set of the background gauge field solutions (constant non-Abelian fields) and solutions of the Dirac equation in these fields.

MSC:

81V05 Strong interaction, including quantum chromodynamics
81T13 Yang-Mills and other gauge theories in quantum field theory
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