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Su(2) gauge field coupled with two massless scalar fields

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From the study of the SU(2) gauge field coupled with two massless scalar fields, we have found solutions to the corresponding YangMills equations. These classical solutions exhibited a form of confinement to an SU(2) gauge charge. Energy expressions of the corresponding gauge and scalar field configurations are obtained. | JOURNAL OF SCIENCE OF HNUE Natural Sci. 2010 Vol. 55 No. 6 pp. 14-19 SU 2 GAUGE FIELD COUPLED WITH TWO MASSLESS SCALAR FIELDS Nguyen Van Thuan Hanoi National University of Education E-mail thuanvatli@yahoo.com Abstract. From the study of the SU 2 gauge field coupled with two massless scalar fields we have found solutions to the corresponding Yang- Mills equations. These classical solutions exhibited a form of confinement to an SU 2 gauge charge. Energy expressions of the corresponding gauge and scalar field configurations are obtained. Keywords gauge field massless scalar field. 1. Introduction Non-abenlian gauge theories were invented by Yang-Mills. Solutions to the classical field equations in which field functions are c-number not operators play an impotant role in investigating the configurations of the corresponding quantum field theory. Based on these solutions applying the semi-classical analysis methods important information about the quantum theory can be obtained which could not be done with the perturbation theory 1-3 . One important result when studying the classical Yang-Mills equations is to recognise that the extremum of the functional in the Euclidian space do not correspond to the zero-unified field but correspond to the nontrivial space-time local field configuration known as instanton 4 . In the quantum theory instantons describe the tunnel effects of the degenerate vacuum states. This result brought a new view to the vacuum structure of the Yang-Mills theory providing a qualitative explanation of the Quark confinement 5-8 . Researches of classical Yang-Mills equations with external sources are well documented. With these kind of problems the most interesting result is to find some particular solutions that can produce screening effects with external color charge similar to the screening effects of the external charge in electrodynamics. Some studies have found that the Quark confinement may have some connections with these screening effects 9 .