Implicit schemes for real-time lattice gauge theory

Area of Science:

• Computational physics
• High-energy physics
• Numerical analysis

Background:

• Classical real-time lattice gauge theory requires stable and accurate numerical methods.
• Simulations of heavy-ion collisions, like those using classical Yang-Mills theory, often face numerical instabilities.
• Existing methods can suffer from dispersion errors, limiting their effectiveness.

Purpose of the Study:

• To develop novel gauge-covariant implicit numerical schemes for classical real-time lattice gauge theory.
• To address and overcome numerical instabilities in three-dimensional classical Yang-Mills simulations.
• To enable accurate wave propagation without numerical dispersion in simulations.

Main Methods:

• Development of new semi-implicit numerical schemes.
• Application of these schemes to three-dimensional classical Yang-Mills simulations.
• Analysis of gauge covariance and Gauss constraint conservation.

Main Results:

• A new semi-implicit scheme effectively cures numerical instabilities.
• The scheme allows for wave propagation free of numerical dispersion along one lattice direction.
• Gauge covariance is maintained, and the Gauss constraint is conserved even with large time steps.

Conclusions:

• The developed numerical schemes are robust and accurate for classical real-time lattice gauge theory.
• These advancements are particularly beneficial for heavy-ion collision simulations.
• The methods provide a reliable framework for future theoretical and computational studies in this field.