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

TL;DR

This paper investigates the chaotic dynamics of classical non-Abelian Yang-Mills fields on a lattice by analyzing the spectra of Kolmogorov-Sinai entropy and complexity, revealing insights into their nonlinearity and chaotic behavior.

Contribution

It introduces a novel analysis of the nonlinearity of non-Abelian lattice gauge fields using entropy and complexity spectra, highlighting their chaotic properties.

Findings

Chaotic behavior observed in lattice Yang-Mills fields.

Spectra of Kolmogorov-Sinai entropy and complexity characterize nonlinearity.

Time-dependent entropy-energy relations elucidate field dynamics.

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