Transport Theories for Strongly-Interacting Systems: Applications to Heavy-Ion Collisions

Preface
Acknowledgements
Contents
About the Author
Acronyms
List of Figures
1 Introduction
	References
2 Nonrelativistic On-Shell Kinetic Theories
	2.1 Time Evolution of N-body Interacting Fermi Systems
	2.2 The Density-Matrix Formalism
		2.2.1 Separation of Correlation Functions
		2.2.2 Expansion Within a Single-Particle Basis
		2.2.3 Conservation Laws
	2.3 The Vlasov Equation
	2.4 The Collision Term According to Uehling-Uhlenbeck
		2.4.1 The Vlasov–Uehling–Uhlenbeck  (VUU) Equation
	2.5 Including Higher Order Interactions
		2.5.1 Definition of Selfenergies
		2.5.2 Effective Parametrizations for the G-matrix
		2.5.3 Coupled-Channel Transport Equations
	2.6 Numerical Solutions
		2.6.1 Application to Low Energy Heavy-Ion Reactions
		2.6.2 Summary
	Solution of Exercises
	References
3 Relativistic On-Shell Kinetic Theories
	3.1 Covariant Transport Equations
		3.1.1 Wigner Transformation  and Gradient Expansion
		3.1.2 Nuclear Equation of State  in the QHD Model
		3.1.3 The Local-Ensemble Method for the Solution of Binary Collision Terms
		3.1.4 Application of RBUU to Au+Au Collisions at 1 A GeV
	3.2 Multi-Particle Transitions
		3.2.1 Baryon-Antibaryon Annihilation and Recreation
		3.2.2 Numerical Implementation
	Solution of Exercises
	Solution of Exercises
	References
4 Relativistic Dynamics and Off-Shell Transport
	4.1 Relativistic Formulations
		4.1.1 Two-Point Functions on the CTP
		4.1.2 The Dyson–Schwinger  Equation on the CTP
		4.1.3 Kadanoff–Baym  Equations
		4.1.4 Definition of Selfenergies
		4.1.5 Application to the Scalar ϕ4-Theory
		4.1.6 Homogeneous Systems in Space
		4.1.7 The Spectral Function
		4.1.8 Results in First-Order Gradient Expansion
		4.1.9 The Equilibrium Distribution
	4.2 Full Versus Approximate Dynamics
		4.2.1 Derivation of the Quantum Boltzmann Approximation
		4.2.2 Boltzmann vs. Kadanoff–Baym  dynamics
	4.3 Derivation of Off-Shell Relativistic Transport Theory
		4.3.1 Kadanoff–Baym  Transport
		4.3.2 Transport in the Botermans–Malfliet Scheme
		4.3.3 Testparticle Representation
		4.3.4 Model Studies
	4.4 Kadanoff–Baym  Dynamics for Fermions
		4.4.1 Two-Point Functions on the CTP
		4.4.2 Definition of Selfenergies
		4.4.3 Spectral Functions
	4.5 Spectral Evolution of Vector Mesons in Heavy-Ion Collisions  at 2 A GeV
	4.6 Electromagnetic Field Evolution in Ultra-Relativistic Collisions
		4.6.1 Electromagnetic Fields in Au+Au Collisions at s= 200 GeV
		4.6.2 Electromagnetic Fields in Cu+Au Collisions at s= 200 GeV
	Solution of Exercises
	References
A The Time Evolution Operator
	A.1 Schrödinger Picture
	A.2 Heisenberg Picture
	A.3 Interaction or Dirac Picture
B Trace Relations  for n-Body Correlations
C The Two-Body Problem in Vacuum
D Periodic Boundary Conditions
E Phase-Space Integrals
F Kramers–Kronig Relation
G Lorentz Transformations, γ-Matrices, and Dirac-Algebra
	G.1 Lorentz-Goup: Scalars, Vectors, Tensors
	G.2 Dirac Equation and Dirac-Clifford Algebra
	G.3 Solutions of the Free Dirac Equation
	G.4 Quantization of the Free Dirac Field
	G.5 Transformation Properties of Dirac Spinors
	G.6 Green's Function of the Free Dirac Field
H Density-Dependent Relativistic Mean-Field Theory
	H.1 Equations of Motion
	H.2 Thermodynamics and Thermodynamic Consistency
Index