Conserved energy-momentum tensor for real-time lattice simulations

Area of Science:

• High-energy physics
• Computational physics
• Quantum chromodynamics

Background:

• Accurate energy-momentum tensor is crucial for lattice QCD simulations.
• Previous lattice formulations faced challenges with conservation laws and discretization errors.

Purpose of the Study:

• To derive an improved energy-momentum tensor expression for pure glue QCD in a discrete lattice formulation.
• To enhance the accuracy of energy and momentum conservation equations in lattice simulations.

Main Methods:

• Derivation of the energy-momentum tensor in the discrete lattice formulation of pure glue QCD.
• Symmetric time discretization procedure for energy conservation.
• Numerical verification using classical real-time lattice gauge theory simulations.

Main Results:

• The derived expression satisfies the energy conservation continuity equation with minimal numerical errors.
• The momentum conservation equation shows higher accuracy in lattice spacing compared to naive discretization.
• Numerical tests demonstrated one to several orders of magnitude reduction in relative error for both conservation equations.

Conclusions:

• The new formulation significantly improves the accuracy of energy and momentum conservation in lattice QCD.
• This method is expected to advance studies of pre-equilibrium dynamics in ultrarelativistic heavy-ion collisions.
• Applications include more precise extraction of transport coefficients like shear viscosity.