Distribution of Energy Momentum Tensor around Static Charges in Lattice Simulations and an Effective Model (Springer Theses)

Supervisors\' Foreword
Preface
Acknowledgements
Contents
1 Introduction
	1.1 Quantum Chromodynamics
		1.1.1 Asymptotic Freedom
		1.1.2 Chiral Symmetry
		1.1.3 Confinement
	1.2 Flux Tube
		1.2.1 Dual Abelian-Higgs Model
		1.2.2 Dynamics of Strings
		1.2.3 Lattice Approach
	1.3 Phase Transition and Exploration of Deconfined Phase
	1.4 Purpose
		1.4.1 Lattice Study
		1.4.2 Effective Model
	1.5 Organization
	References
2 Energy Momentum Tensor
	2.1 Derivation and Properties of Energy Momentum Tensor
		2.1.1 Derivation and Properties
		2.1.2 Physical Meanings
		2.1.3 Example: Energy Momentum Tensor in Pure Gauge Theory
	2.2 Energy Momentum Tensor in Maxwell Theory
		2.2.1 Maxwell Equations and Classical System
		2.2.2 Energy Conservation
		2.2.3 Momentum Conservation
		2.2.4 Maxwell Stress and Coulomb Force
		2.2.5 Stress Distribution on Source Plane
	References
3 Lattice Field Theory
	3.1 Feynman Path Integral
	3.2 Lattice Regularization
		3.2.1 Simple Example
		3.2.2 Free Boson Field
		3.2.3 Free Fermion Field
	3.3 Lattice Gauge Theory
		3.3.1 Gauge Principle and Gauge Field
		3.3.2 Link Variable
		3.3.3 Path Integral
		3.3.4 Non-Abelian Gauge Theory on the Lattice
	3.4 Gauge-Invariant Quantity on the Lattice
		3.4.1 Wilson Loop
		3.4.2 Polyakov Loop
	References
4 Yang–Mills Gradient Flow and Energy Momentum Tensor
	4.1 Quantum Theory of Yang–Mills Theory
		4.1.1 Action
		4.1.2 Quantization
		4.1.3 One-Loop Divergences
		4.1.4 Renormalization
	4.2 Introduction to Gradient Flow
		4.2.1 Idea of Yang–Mills Gradient Flow
		4.2.2 Perturbative Expansion of Gradient Flow
		4.2.3 Example: Two-Point Function of Flowed Gauge Field
	4.3 Proof of Renormalizability of Gradient Flow
		4.3.1 (D+1)-Dimensional Field Theory
		4.3.2 BRS Invariance and WT Identity of (D+1)-Dimensional System
		4.3.3 Proof of Renormalizability
	4.4 Application to Energy Momentum Tensor
		4.4.1 Small Flow Time Expansion
		4.4.2 Renormalization Group Equation and Expansion Coefficients
		4.4.3 Energy Momentum Tensor on the Lattice
	4.5 Comments on Fermions
	References
5 Distribution of Energy Momentum Tensor around Single Static Quark in Deconfined Phase of SU(3) Yang–Mills Theory
	5.1 EMT around a Static Quark in SU(3) Yang–Mills Theory on the Lattice
		5.1.1 Correlation
		5.1.2 Spherical Coordinate
	5.2 Lattice Setup
		5.2.1 Gauge Configurations
		5.2.2 Discretization Effect
		5.2.3 Double Extrapolation
	5.3 Results of EMT Distributions
		5.3.1 Channel Dependence
		5.3.2 Temperature Dependence
	References
6 Distribution of Energy Momentum Tensor around  Static Quark–Anti-Quark in Vacuum  of SU(3) Yang–Mills Theory
	6.1 Wilson Loop and QbarQ Potential
		6.1.1 QbarQ Potential
		6.1.2 Determination of NAPE
	6.2 Distribution of Energy Momentum Tensor around QbarQ
		6.2.1 Correlation
		6.2.2 Cylindrical Coordinate
	6.3 Setup
	6.4 EMT Distribution on Source Plane
	6.5 EMT Distribution on Mid-Plane
		6.5.1 Double Extrapolation
		6.5.2 EMT Distribution on Mid-Plane
	References
7 Distribution of Energy Momentum Tensor around Magnetic Vortex  in Abelian-Higgs Model
	7.1 Stress Tensor and Momentum Conservation in Cylindrical Coordinate
	7.2 Abelian-Higgs Model
		7.2.1 Model
		7.2.2 Energy Momentum Tensor in Cylindrical Coordinate System
	7.3 Magnetic Vortex
		7.3.1 Magnetic Vortex with Finite Length
		7.3.2 Infinitely Long Vortex
		7.3.3 Physical Units
		7.3.4 Details of Numerical Analysis
	7.4 Numerical Results
		7.4.1 Infinitely Long Vortex
		7.4.2 Finite-Length Flux Tube
	References
8 Summary and Outlook
	References
Appendix A Improved Estimator
Appendix B Tree-Level Improvement of Lattice Observables
Appendix C Leading-Order Perturbative Analysis of EMT around Single Static Charge
Appendix D Smearing Method
D.1  SU(N) Projection
D.2  APE Smearing
Appendix E Analytic Properties of Abelian-Higgs Model