Nonlinearity of the non-Abelian lattice gauge field theory according to the spectra of Kolmogorov-Sinai entropy and complexity

Abstract

Yang-Mills fields are an important part of the non-Abelian space theory describing the properties of quark-gluon plasma. The dynamics of the classical fields are given by the Hamiltonian equations of motion, which contain the member of the field strength tensor SU(2) \cite{1.}. This system exhibits chaotic behavior. The homogeneous Yang-Mills equation includes the quadratic part of the field strength tensor $F_{\mu \nu }^a$ expressed in Minkowski space, which was determined by the fields $A_{\mu }^a$. The dynamics of the classical Yang-Mills field equations arise from the Hamiltonian SU(2) field tensor so that the total energy remains constant and fulfills the Gaussian law. The microcanonical equations of motion are solved on a lattice $N^d$, which shows chaotic dynamics and we research the time-dependent entropy-energy relation on the lattice, which can be shown by the spectrum of Kolmogorov-Sinai entropy and the statistical complexity