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Electric/magnetic flux tube on the background of magnetic/electric field. (English) Zbl 1049.78005

The author studies the phenomenon of confinement of quarks in quantum chromodynamics. This phenomenon is connected with a hypothetical flux tube filled with color electric field and stretched between quark and antiquark. The confinement is a non-perturbative effect, it means that it cannot be derived using traditional theoretical methods of quantum field theory – the Feynman diagram technique. The author gives arguments that the phenomenon of a flux tube in quantum chromodynamics is closely connected with a spontaneously symmetry breakdown of gauge theory. It is shown that in the presence of a mass term in the \(SU(2)\) gauge theory the Nielsen-Olesen equations \[ K^{\prime\prime }+x^{-1}K^{\prime }=Kw^2+(1/2)K(K^2-m^2), \;\;w^{\prime\prime }+x^{-1}w^{\prime }-x^{-2}w =wK^2 \] describe the flux tube surrounded by an external field. The functions \(K\) and \(w\) are the modified gauge potentials \(A_{\mu }^{a}\) considered in cylindrically symmetric case with cylindrical coordinates \(\rho \), \(z\), \(\varphi \), and \(x=\rho m\sqrt{2}\). The quantity \(m=m(1)=m(2)\) comes from the term \(m^2(a)A_{\mu }^{a}\) which is the consequence of the quantization leading to the gauge symmetry breakdown.

MSC:

78A35 Motion of charged particles
81T13 Yang-Mills and other gauge theories in quantum field theory
81R40 Symmetry breaking in quantum theory
81V05 Strong interaction, including quantum chromodynamics
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