Time-Dependent Variational Approach to the Non-Abelian Pure Gauge Theory

TL;DR

This paper develops a time-dependent variational method in the Schrödinger picture for pure Yang-Mills theory, deriving transport coefficients like shear viscosity and finding quantum gluons contribute zero at lowest order.

Contribution

It introduces a Gaussian wave functional variational approach for non-Abelian gauge theories and applies it to compute transport properties.

Findings

Quantum gluons contribute zero to shear viscosity at lowest order.

The variational approach provides equations of motion in Liouville-von Neumann form.

Transport coefficients can be derived using linear response theory.

Abstract

The time-dependent variational approach to the pure Yang-Mills gauge theory, especially a color su(3) gauge theory, is formulated in the functional Schroedinger picture with a Gaussian wave functional approximation. The equations of motion for the quantum gauge fields are formulated in the Liouville-von Neumann form. This variational approach is applied in order to derive the transport coefficients, such as the shear viscosity, for the pure gluonic matter by using the linear response theory. As a result, the contribution to the shear viscosity from the quantum gluons is zero up to the lowest order of the coupling g in the quantum gluonic matter.