SELF DUAL SOLUTIONS OF CLASSICAL YANG-MILLS THEORY

Tóm tắt

In this paper, we investigate self dual solutions in Minkowski space of the classical SU(2) Yang-Mills theory. Self dual fields automatically satisfy the motion equations of the pure gauge theory. We present a self dual solution of the pure SU(2) Yang-Mills theory. This solution is imaginary and exhibits to break the local SU(2) symmetry at large distance. From the connection between the pure SU(2) gauge theory and the scalar theory, we obtain formulas for several interesting quantities: the Yang-Mills field strengths, the Lagrangian density, the energy-momentum tensor. The obtained results prove clearly that if fields are self dual then energy-momentum tensor equals zero. We also find a self dual solution of the corresponding field equation. We see that the spatial component of the SU(2) gauge potential is analogous to the potential of a point magnetic monopole.