Quasiself-dual fields in $N=4$ supersymmetric Yang–Mills theory

In Euclidean conformally invariant Yang–Mills theory with sextuplet of scalar fields – the bosonic sector of $N=4$ supersymmetric Yang–Mills theory – a general representation of the quasiself-dual gauge field in terms of the multiplet of scalar fields is found. In the case of $O(4)$ symmetry the model generates a Hamiltonian system with two degrees of freedom, for which a description of the quasiselfdual fields in the framework of the Hamilton–Jacobi method is obtained. An explicit example of a quasi-instanton in the region $g^2<0$ is constructed.