Inhalt

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   Contents
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  1 Preface
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   1.1 Introduction
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   1.2 Overview of the Thesis
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   1.3 Units and Conventions
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   I Theoretical Foundations
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  2 Discretization of Quantum Field Theories
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  2.1 Classical Scalar and Vector Fields
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   2.1.1 Action and Lagrangian
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   2.1.2 The Klein-Gordon theory
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   2.1.3 The Dirac theory
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  2.2 Path Integral Quantization
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   2.2.1 Hamiltonian version of the path integral
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   2.2.2 Lagrangian version of the path integral
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   2.3 Quantum electrodynamics
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   2.4 Quantum chromodynamics
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   2.5 Wick rotation
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   2.6 Lattice discretization
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   2.7 The Wilson gauge action and improvements
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  3 Fermions on the lattice
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  3.1 Naive Fermions
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   3.1.1 Symmetries of the naive action
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   3.1.2 The doubling problem
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  3.2 Staggered fermions
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   3.2.1 The staggered transformation
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   3.2.2 Symmetry properties of staggered fermions
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   3.2.3 Momentum, spin and taste operators for staggered fermions
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  4 Simulation of lattice gauge theories
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   4.1 Wick's theorem
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   4.2 MCMC/Sampling of Monte-Carlo data
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   4.2.1 Metropolis algorithm
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   4.2.2 Hybrid-Monte-Carlo algorithm
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   4.3 Rooting
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  4.4 Smoothing techniques
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   4.4.1 Gradient flow
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   4.4.2 Smearing of the gauge field
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   4.4.3 Smearing of the fermions sources
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  5 Data analysis
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   5.1 Treating of statistical uncertainties
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   5.1.1 Blocking
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   5.1.2 Bootstrap resampling
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   5.1.3 Jackknife resampling
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   5.2 Treating of systematic uncertainties
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   5.3 Fitting procedure
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   5.3.1 chi-squared
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   5.3.2 Evidence for the quality of fits
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   5.4 Statistical and systematic covariances
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   5.5 Generalized Eigenvalue problems
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   II Application to Standard Model Tests
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  6 Lattice techniques
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   6.1 Action and ensembles
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   6.2 Gradient flow based scale setting
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   6.3 Meson mass and decay constant on the lattice
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   6.4 Finite volume effects of pseudo-scalar masses and decay constants
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   6.5 Strong isospin-breaking and QED contributions
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   6.6 Omega operators and correlation functions
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   6.7 Extraction of the Omega-baryon mass
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  7 Global analysis
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   7.1 Schemes, transformations and global fit functions
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   7.2 Global fit procedure
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   7.2.1 Isospin symmetric
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   7.2.2 isospin-breaking
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   7.2.3 Sea quark contributions
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  7.3 Further aspects of the analysis
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   7.3.1 Weighting of the systematics
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   7.3.2 Blinding and cross checks
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  8 Lattice results
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   8.1 Computation of the pseudo-scalar decay constant ratio
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   8.2 Computation of wnull
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   8.3 Computation of wnull
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   8.4 Computation of tnull
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  9 Phenomenology
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   9.1 The anomalous magnetic moment of the muon
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  9.2 Lattice computation of fkfpi as a test for the CKM-unitarity
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   9.2.1 The CKM unitarity and its relation to the meson decay constants
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   9.2.2 Phenomenological consequences of the lattice results
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   9.3 Discrepancies in scale setting
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  10 Exploratory techniques
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   10.1 Two pion contribution to vector mesons
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   10.2 Implementation
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   10.2.1 Vector meson correlator
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   10.2.2 Free pion diagram
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   10.2.3 Interaction diagram
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   10.2.4 Connected pion diagram
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   10.3 Decomposition of the vector-like states and reconstruction of the vector propagator
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   10.4 Summary and comment on the further progress
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   11 Conclusion and Outlook
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   III Appendices
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  12 Supplementary Material
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   12.1 Projective representations
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   12.2 Central Group Extensions
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   12.3 Generelization of Wigner's Little Group Procedure
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   12.4 Grassmann algebra
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   Bibliography