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Gagliardi, Giuseppe: The QCD Phase Diagram from Strong Coupling Expansion. 2020
Inhalt
Declaration of Authorship
Abstract
Introduction
QCD at finite temperature and density: a short review
The continuum theory
QCD at finite temperature
QCD at finite density
Chiral symmetry and confinement
The lattice formulation
From continuum to discrete
Recovering the continuum theory
The naive fermion discretization
Wilson fermions
Staggered fermions
Gauge fields
Numerical methods
Dual representations
Definition and general considerations
The lattice Schwinger model
Formulation
Grassmann and gauge integration
The dual partition function
Lattice QCD at strong coupling
The dual formulation
Analysis of the sign problem and the finite density phase diagram
Gauge integration
Beyond strong coupling: the polynomial one-link integral
Solution of the polynomial one-link integral
Properties of the Weingarten functions
The decoupling operators and the DOI
The irreducible matrix elements
Final form of the polynomial 1-link integral
Recovering the strong coupling one-link integral
The dual representation at finite
Dualization in Yang-Mills theory
Dualization including staggered fermions
Formulation and main properties
The fermionic sign
Observables
Improving the Taylor expansion
Analysis of the corrections
Partition function at O()
Partition function at O(2)
Cross checks from exact enumeration
Conclusion
Proof of the combinatorial lemma Eq. (4.18)
List of generalized Weingarten functions
Ariadne-
Acknowledgements