tailieunhanh - Some properties of Su(2) yang mills theory connecting with o4 theory

In this paper we consider some properties of the SU(2) YangMills theory connecting with scalar o4 theory. In the case when scalar field φ is time independent, we find explicit solutions to equations of motion for corresponding o4 theory. The spatial component of the SU(2) Yang-Mills potential corresponding with this solution is like potential of point magnetic monopole. | JOURNAL OF SCIENCE OF HNUE Natural Sci. 2011 Vol. 56 No. 7 pp. 72-77 SOME PROPERTIES OF SU 2 YANG-MILLS THEORY CONNECTING WITH φ4 THEORY Nguyen Van Thuan Hanoi National University of Education E-mail thuanvatli@ Abstract. In this paper we consider some properties of the SU 2 Yang- Mills theory connecting with scalar φ4 theory. In the case when scalar field φ is time independent we find explicit solutions to equations of motion for corresponding φ4 theory. The spatial component of the SU 2 Yang-Mills potential corresponding with this solution is like potential of point magnetic monopole. Keywords Gauge field theory scalar field theory. 1. Introduction Non-Abelian gauge theory offer the greatest promise to describe the elemen- tary forces in nature 1 . We investigate here the solutions to the classical Yang-Mills equations they are non-Abelian field equations. However solutions to non-linear field equations are notoriously difficult to fine since there exists no general method for discovering them. The usual approach is to make some guess as to the form of the solution and insert it in to the field equations to see if it solves them. Accord- ing to this approach one have found some exact solutions to the Yang-Mills field equations 2-6 . Besides the above approach one sees that there exists a connection between the SU 2 Yang-Mills theory and scalar φ4 theory. From this connection one reduces the complicated equations of motion of the Yang-Mills theory to the sin- gle equation of motion for scalar φ4 theory. Therefore one can find some properties of the Yang-Mills theory 7-9 . 2. Content . Equations of motion of the SU 2 Yang-Mills field Yang-Mills fields can be introduced in the following fashion. Consider a multi- plet ψ x which transforms locally under the action of some gauge group G according to the rule ψ x ψ x ω x ψ x 72 Some properties of SU 2 Yang-Mills theory connecting with φ4 theory where ω x belongs to the relevant representation of G. Let