Inhalt

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   Table of contents
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   List of figures
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   List of tables
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   1 Introduction
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  1.1 Quantum Chromodynamics
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   1.1.1 Historical development
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   1.1.2 QCD action
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   1.1.3 QCD Path Integral
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   1.1.4 QCD: Energy scale dependence description
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  2 Scattering Theory
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   2.1 Introduction
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   2.2 S-matrix formalism
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   2.2.1 Case study: 22 scattering with equal masses
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   2.2.2 Pole structure
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   2.2.3 Resonances
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   2.2.4 Resonant transition form factors
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  3 Lattice methods
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   3.1 Wick rotation
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   3.2 Lattice Regularization
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   3.2.1 Wilson Discretization
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   3.2.2 Symanzik Improvement
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   3.2.3 Other discretization schemes
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   3.2.4 Observables on the lattice
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  3.3 Lattice Simulations
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   3.3.1 Monte Carlo
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   3.3.2 Solvers
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   3.3.3 Error estimates
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  3.4 Machine Learning techniques for the study of statistical systems
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   3.4.1 Introduction
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   3.4.2 The Ferromagnetic 2-Dimensional Ising Model
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   3.4.3 Deep Learning Autoencoders
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   3.4.4 Results
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   3.4.5 The latent dimension per configuration
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   3.4.6 The absolute average latent dimension
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   3.4.7 The Latent Susceptibility and the Critical Temperature
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   3.4.8 Conclusion
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   4 Hadron spectroscopy on the lattice
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   4.1 Angular momentum on the lattice
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   4.1.1 Center of Mass frame
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   4.1.2 Moving frames
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  4.2 Interpolating field operators
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   4.2.1 Single Hadron Interpolators
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   4.2.2 Two-Hadron Interpolators
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   4.3 Correlation functions
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   4.3.1 Building blocks for the correlation functions
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  4.4 Signal enhancement methods
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   4.4.1 Extended source
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  4.5 Link Smearing
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   4.5.1 APE smearing
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   4.5.2 Stout Smearing
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   4.6 Variational method
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  4.7 Elastic scattering of two particles in a finite volume
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   4.7.1 Kinematics
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   4.7.2 Lüscher formalism
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   4.8 Spectrum interpretation: After taking FV effects
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   4.9 Resonance photoproduction
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   4.9.1 Transition form factor
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  5 Meson resonances & photoproduction
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   5.1
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   5.1.1 Motivation
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   5.1.2
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   5.1.3 Lattice parameters
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   5.1.4 Interpolating fields and two-point functions
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   5.1.5 Spectrum results
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   5.1.6 The Lüscher analysis: formalism
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   5.1.7 The Lüscher analysis: results
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  5.2 transition & radiative decay
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   5.2.1 Introduction
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   5.2.2
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   5.2.3 Correlation functions
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   5.2.4 Optimized three-point functions
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   5.2.5 Determining the finite volume matrix elements
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   5.2.6 Mapping from finite volume to infinite volume
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   5.2.7 Fitting the amplitude V
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   5.2.8 Observables
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   5.2.9 Conclusion
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  6 Towards Resonance & photoproduction
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   6.1 resonance
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   6.1.1 Interpolators and correlation functions
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   6.1.2 Spectrum results
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   6.1.3 Lüscher Analysis: Phase shift fit results
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   6.2 Conclusion
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  7 Conclusion
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   7.1 Summary of results
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   7.2 Outlook
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   References
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   Appendix A Murray Gell-Mann matrices