Projection and nested force-gradient methods for quantum field theories / vorgelegt von Dmitry Shcherbakov, geboren in Wolgograd, Russland. Wuppertal, 26. Juli 2017
Inhalt
- ACKNOWLEDGMENTS
- CONTENTS
- LIST OF FIGURES
- 1 MOTIVATION AND OVERVIEW
- 2 GEOMETRIC NUMERICAL INTEGRATORS
- 2.1 Geometric time integration of ODEs
- 2.2 Hamiltonian mechanics
- 2.3 Conservation of physical properties
- 2.3.1 Symmetry, time-reversibility
- 2.3.2 Volume-preservation, symplecticity
- 2.3.3 Energy conservation, convergence order
- 2.4 Backward error analysis
- 2.5 Numerical time integrators for ODEs
- 2.5.1 Splitting and composition methods
- 2.5.2 Runge-Kutta methods
- 2.5.3 Projection methods
- 2.5.4 Variational methods
- 2.5.5 Linear multistep methods
- 2.6 Numerical integration on Lie groups
- 3 QUANTUM FIELD THEORIES ON THE LATTICE
- 3.1 Basic concepts of quantum field theories
- 3.2 Regularization on the lattice
- 3.3 Hybrid Monte Carlo algorithm
- 4 PROJECTION METHODS
- 4.1 Introduction in the projection methods
- 4.2 Another view on symmetric projection schemes
- 4.3 The Structure-preserving approach
- 4.4 Structure-preserving approach (= (h))
- 4.5 Linear projection methods
- 4.6 Conclusion
- 5 NESTED FORCE-GRADIENT METHODS
- 5.1 Splitting decomposition schemes
- 5.2 Force-gradient decomposition method
- 5.3 Multirate approach
- 5.4 Nested force-gradient schemes
- 5.5 Adapted nested force-gradient schemes
- 6 NUMERICAL RESULTS
- 7 SUMMARY AND OUTLOOK
- A Shadow Hamiltonian for the projection methods with =(h)
- B Shadow Hamiltonian for the projection methods with 1=1(h) and 2=2(h)
- C Shadow Hamiltonian for linear projection methods with =(h)