Geometric integration on Lie groups and its applications in lattice QCD / vorgelegt von Michèle Wandelt. Wuppertal, 7. Februar 2020
Inhalt
- Contents
- List of Figures
- 1 Introduction
- I Foundations
- 2 Lattice QCD and Differential Equations
- 2.1 Gauge Fields in Lattice QCD
- 2.2 Hamiltonian Equations of Motion
- 2.2.1 The Hamiltonian
- 2.2.2 Hamiltonian Equations of Motion.
- 2.2.3 Derivation of the Hamiltonian Equations of Motion
- 2.2.4 Structure of the Hamiltonian Equations of Motion.
- 2.3 Hybrid Monte Carlo Method
- 2.4 The Wilson Flow
- 2.5 Summary
- 3 Numerical Integration of Differential Equations on Lie Groups
- II Developments in Lie Group Methods
- 4 Runge-Kutta Methods for Lie Groups
- 4.1 Step Size Control
- 4.1.1 Step Size Prediction for the Abelian Case
- 4.1.2 Step Size Control for Munthe-Kaas Runge-Kutta Schemes
- 4.2 The Cayley Transform
- 4.2.1 The Cayley Transform as Local Parameterization
- 4.2.2 Numerical Integration with the Cayley Mapping
- 4.3 Summary
- 5 Geometric Numerical Integration
- 5.1 Geometric Integration
- 5.2 Störmer-Verlet or Leapfrog Method
- 5.3 Symmetric Partitioned Runge-Kutta Methods
- 5.4 Time-reversible Projection Schemes
- 5.5 Summary
- 6 Exponential Smoothing Splines
- III Simulation
- 7 HMC in Lattice QCD
- 7.1 HMC Simulations on Lattice Gauge Fields
- 7.2 Geometric Integration Methods
- 7.2.1 Leapfrog Method
- 7.2.2 The Cayley-Leapfrog Method
- 7.2.3 The Symmetric Partitioned Runge-Kutta Method
- 7.2.4 The Time-Reversible Projection Method
- 7.3 Summary
- 8 The Wilson Flow and Finite Temperature QCD
- 8.1 The Model
- 8.2 Step Size Control for Munthe-Kaas Runge-Kutta Methods
- 8.3 Energy Difference Method for the Critical Temperature
- 8.4 Summary
- 9 Conclusion and Outlook
- Acknowledgements
- 10 Appendix