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Table of Contents
Intro
Contents
About the Editors
1 Strongly Interacting Matter Under Rotation: An Introduction
1.1 Milestones
1.2 Introduction
1.3 Accessing Subatomic Vorticity
1.4 From Signal to Physics
1.4.1 Hydrodynamics as the Basis to Understand Hyperon Polarization
1.4.2 Vector Meson Spin Alignment-More Complicated Physics?
1.4.3 Future Experimental Work
1.5 Summary and Outlook
2 Polarization in Relativistic Fluids: A Quantum Field Theoretical Derivation
2.1 Introduction
2.2 The Spin Density Matrix and the Definition of Mean Spin
2.3 The Single-Particle Limit and Global Equilibrium Factorization
2.4 The Covariant Wigner Function
2.4.1 The Scalar Field
2.4.2 The Dirac Field
2.5 Fermion Polarization and the Covariant Wigner Function
2.6 Polarization From the Angular Momentum Operator
2.7 Local Thermodynamic Equilibrium
2.7.1 Polarization at Local Thermodynamic Equilibrium
2.8 Summary and Outlook
3 Thermodynamic Equilibrium of Massless Fermions with Vorticity, Chirality and Electromagnetic Field
3.1 Introduction
3.2 General Global Equilibrium with Electromagnetic Field
3.2.1 Vanishing Electromagnetic Field
3.3 Dirac Field in External Electromagnetic Field
3.3.1 Symmetries in Constant Electromagnetic Field
3.4 Chiral Fermions in Constant Magnetic Field
3.4.1 Exact Thermal Solutions
3.4.2 Thermodynamic Potential
3.4.3 Chiral Fermion Propagator in Magnetic Field
3.4.4 Electric Current Mean Value
3.4.5 Axial Current Mean Value
3.5 Constant Vorticity and Electromagnetic Field
3.5.1 Expansion on Thermal Vorticity
3.5.2 Currents and Chiral Anomaly
4 Exact Solutions in Quantum Field Theory Under Rotation
4.1 Introduction
4.2 Relativistic Kinetic Theory
4.2.1 Rigidly Rotating Thermal Distribution
4.2.2 Macroscopic Quantities
4.3 Quantum Rigidly Rotating Thermal States
4.4 Mode Solutions in Cylindrical Coordinates
4.5 Quantum Stationary Thermal Expectation Values
4.5.1 Fermion Condensate
4.5.2 Charge Current
4.5.3 Stress-Energy Tensor
4.6 Quantum Rigidly Rotating Thermal Expectation Values
4.6.1 Fermion Condensate
4.6.2 Charge Current
4.6.3 Axial Current
4.7 Hydrodynamic Analysis of the Quantum Stress-Energy Tensor
4.7.1 Stress-Energy Tensor Expectation Values
4.7.2 Thermometer Frame
4.7.3 Quantum Corrections to the SET
4.8 Rigidly Rotating Quantum Systems in Curved Space-Time
4.9 Summary
5 Particle Polarization, Spin Tensor, and the Wigner Distribution in Relativistic Systems
5.1 Introduction
5.2 Relativistic Kinetic Theory and Its Limitations
5.3 The Relativistic Spin Tensor as a Polarization Sensitive Macroscopic Object
5.4 Particle Polarization, the Wigner Distribution, and the Polarization Flux Pseudotensor
5.5 Summary
6 Quantum Kinetic Description of Spin and Rotation
6.1 Introduction
Contents
About the Editors
1 Strongly Interacting Matter Under Rotation: An Introduction
1.1 Milestones
1.2 Introduction
1.3 Accessing Subatomic Vorticity
1.4 From Signal to Physics
1.4.1 Hydrodynamics as the Basis to Understand Hyperon Polarization
1.4.2 Vector Meson Spin Alignment-More Complicated Physics?
1.4.3 Future Experimental Work
1.5 Summary and Outlook
2 Polarization in Relativistic Fluids: A Quantum Field Theoretical Derivation
2.1 Introduction
2.2 The Spin Density Matrix and the Definition of Mean Spin
2.3 The Single-Particle Limit and Global Equilibrium Factorization
2.4 The Covariant Wigner Function
2.4.1 The Scalar Field
2.4.2 The Dirac Field
2.5 Fermion Polarization and the Covariant Wigner Function
2.6 Polarization From the Angular Momentum Operator
2.7 Local Thermodynamic Equilibrium
2.7.1 Polarization at Local Thermodynamic Equilibrium
2.8 Summary and Outlook
3 Thermodynamic Equilibrium of Massless Fermions with Vorticity, Chirality and Electromagnetic Field
3.1 Introduction
3.2 General Global Equilibrium with Electromagnetic Field
3.2.1 Vanishing Electromagnetic Field
3.3 Dirac Field in External Electromagnetic Field
3.3.1 Symmetries in Constant Electromagnetic Field
3.4 Chiral Fermions in Constant Magnetic Field
3.4.1 Exact Thermal Solutions
3.4.2 Thermodynamic Potential
3.4.3 Chiral Fermion Propagator in Magnetic Field
3.4.4 Electric Current Mean Value
3.4.5 Axial Current Mean Value
3.5 Constant Vorticity and Electromagnetic Field
3.5.1 Expansion on Thermal Vorticity
3.5.2 Currents and Chiral Anomaly
4 Exact Solutions in Quantum Field Theory Under Rotation
4.1 Introduction
4.2 Relativistic Kinetic Theory
4.2.1 Rigidly Rotating Thermal Distribution
4.2.2 Macroscopic Quantities
4.3 Quantum Rigidly Rotating Thermal States
4.4 Mode Solutions in Cylindrical Coordinates
4.5 Quantum Stationary Thermal Expectation Values
4.5.1 Fermion Condensate
4.5.2 Charge Current
4.5.3 Stress-Energy Tensor
4.6 Quantum Rigidly Rotating Thermal Expectation Values
4.6.1 Fermion Condensate
4.6.2 Charge Current
4.6.3 Axial Current
4.7 Hydrodynamic Analysis of the Quantum Stress-Energy Tensor
4.7.1 Stress-Energy Tensor Expectation Values
4.7.2 Thermometer Frame
4.7.3 Quantum Corrections to the SET
4.8 Rigidly Rotating Quantum Systems in Curved Space-Time
4.9 Summary
5 Particle Polarization, Spin Tensor, and the Wigner Distribution in Relativistic Systems
5.1 Introduction
5.2 Relativistic Kinetic Theory and Its Limitations
5.3 The Relativistic Spin Tensor as a Polarization Sensitive Macroscopic Object
5.4 Particle Polarization, the Wigner Distribution, and the Polarization Flux Pseudotensor
5.5 Summary
6 Quantum Kinetic Description of Spin and Rotation
6.1 Introduction