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Implicit schemes for real-time lattice gauge theory.

Andreas Ipp1, David Müller1

  • 1Institut für Theoretische Physik, Technische Universität Wien, 1040 Vienna, Austria.

The European Physical Journal. C, Particles and Fields
|January 15, 2019
PubMed
Summary

We developed new numerical methods for lattice gauge theory simulations. These methods improve stability and accuracy in heavy-ion collision models, conserving constraints for better real-time predictions.

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.

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  • 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.