Wissel, Sönke: Mesonic correlation functions from light quarks and their spectral representation in hot quenched lattice QCD. 2006
Inhalt
- Introduction
- 1 Quantum Chromodynamics in the continuum
- 1.1 QCD at finite temperature
- 1.2 Symmetries of the Lagrangian
- 1.3 Phases in finite temperature QCD in theoretical framework
- 1.3.1 Phases at vanishing density
- 1.3.2 Chiral condensate and the Dirac eigenvalue spectrum
- 1.3.3 Phases at finite density
- 1.4 Finite temperature QCD in experimental framework
- 2 QCD on the lattice - A brief introduction
- 2.1 The lattice as a regulator of QCD
- 2.2 Gauge fields on the lattice
- 2.3 Matter fields on the lattice
- 2.3.1 Fermion doublers and Nielsen-Ninomiya theorem
- 2.3.2 Wilson fermions
- 2.3.3 Wilson fermions with Symanzik improvement (Sheikholeslami-Wohlert action)
- 2.3.4 Staggered fermions
- 2.3.5 The Ginsparg-Wilson relation and the overlap operator
- 2.3.6 Hypercube fermions
- 2.4 Simulation techniques
- 2.4.1 Quenched approximation
- 2.4.2 Markov chains and Metropolis
- 2.4.3 Heat bath and overrelaxation
- 2.4.4 Inversion of the fermion matrix
- 2.4.5 Errors and fitting
- 2.5 Z(3)-Symmetry on the lattice
- 2.6 Evaluating physical quantities on the lattice
- 2.7 Simulation details
- 2.8 Mesonic correlation and spectral functions
- 3 Maximum entropy method with free data
- 3.1 Bayes' theorem and maximum entropy method
- 3.2 Free correlation functions in their spectral representation
- 4 Analysis of mesonic properties below and above Tc
- 4.1 Extracting masses and energies from correlation functions
- 4.1.1 Masses and energies from temporal correlation functions
- 4.1.2 Masses in the chiral limit
- 4.1.3 Dispersion relations
- 4.2 Bethe-Salpeter amplitudes and the pion radius
- 4.3 Quark masses from axial Ward identities
- 4.4 Decay constants
- 4.5 Spectral functions
- 4.6 Cut-off and thermal effects in temporal correlation functions
- 5 Screening masses and correlation functions in the high-temperature phase
- 5.1 Screening masses in infinite volume and continuum extrapolation
- 5.2 Spatial correlation function in the context of chiral and Lorentz symmetry breaking
- Summary, conclusions and outlook
- A Conventions
- B Tables of results
- B.1 AWI quark masses below Tc
- B.2 AWI quark masses above Tc
- B.3 Renormalization group factors
- B.4 Screening masses
- B.5 MEM pole masses
- C Auxiliary Functions for the Free Lattice Field Theory
- D Storing data - Database SQL with MySQL
- List of
- References
- Acknowledgments
- Selbstständigkeitserklärung
- Curriculum vitæ