Cover

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Title

Copyright

Contents

Preface

1 Introduction

1.1 Quantum chromodynamics

1.2 The deconfinement/chiral transition

1 The bag model

2 Lattice quantum chromodynamics

1.3 Heavy ion collisions

References and further reading

Exercises

2 Quantum statistical mechanics

2.1 Path integral formalism and imaginary time

2.2 Operator formalism

2.3 The spectral function ρ(k0)

2.4 The Matsubara (or imaginary-time) propagator

2.5 The time-ordered propagator

2.6 Frequency sums

References and further reading

Exercises

3 The scalar field at finite temperature

3.1 The neutral scalar field

1 Wick's theorem and the propagator

2 First-order corrections: propagator and partition function

3 Feynman rules

3.2 The charged scalar field

3.3 Real-time formalism

1 Path integrals

2 Integration path and propagators

3 Feynman rules with the symmetric propagator

3.4 The self-energy in the real-time formalism

3.5 Renormalization at non-zero temperature

References and further reading

Exercises

4 Simple applications of perturbation theory

4.1 Ring diagrams in the φ4-model

4.2 Some one-loop diagrams

1 Self-energy diagram in the imaginary-time formalism

2 Self-energy diagram in the real-time formalism

3 The three-point vertex at one-loop

4.3 Cutting rules at finite temperature

1 Derivation of the rules

2 Application to the self-energy

4.4 Physical interpretation of discontinuities

1 Production of a weakly interacting massive particle

2 Production of a weakly interacting massless particle

3 General proof

4 Small deviations from equilibrium

References and further reading

Exercises

5 Dirac and gauge fields at finite temperature

5.1 The Dirac field at finite temperature

1 Coherent fermion states and path integrals

2 Quantization of the Dirac field

3 Frequency sums

4 Non-zero chemical potential

5.2 Quantization of gauge fields at non-zero temperature

1 The partition function

2 The gauge boson propagator in linear gauges

3 The gauge boson propagator at non-zero temperature

5.3 Real photon and lepton pair production

1 Real photon production

2 Lepton pair production

References and further reading

Exercises

6 Collective excitations in a plasma

6.1 Linear response theory

6.2 The photon propagator in a QED plasma

1 General form of the photon propagator

2 The hard thermal loop approximation for Πμν

3 Evaluation of Πμν

4 Transverse and longitudinal photons

6.3 Debye screening and plasma oscillations

1 Linear response and Debye screening

2 Plasma oscillations

3 Sum rules and residues

4 Non-zero chemical potential

6.4 Kinetic derivation of the photon self-energy

6.5 The electron propagator in a QED plasma

1 Evaluation of Σ

2 Quasi-particles

6.6 Elementary excitations in a QCD plasma

References and further reading

Exercises

7 Hard thermal loops and resummation

7.1 Hard thermal loops in QED

1 The three-point function in QED

2 The four-point functions in QED

3 The effective Lagrangian in QED

7.2 The QCD plasma

1 The three-point functions in QCD

2 General remarks on hard thermal loops

3 Hard thermal loops from Ward identities

7.3 The effective expansion

1 General theory

2 Production of soft dileptons in a quark-gluon plasma

3 The gluon damping rate

4 Higher-order calculations

7.4 Kinetic theory of hard thermal loops

References and further reading

Exercises

8 Dynamical screening

8.1 Energy loss of a heavy fermion in a QED plasma

8.2 Production of hard real photons from a quark-gluon plasma

8.3 Screening and transport phenomena

References and further reading

Exercises

9 Neutrino emission from stars

9.1 The photon dispersion relations revisited

9.2 Neutrino emission from photon decay

References and further reading

Exercises

10 Infrared problems at finite temperature

10.1 Kinoshita-Lee-Nauenberg theorem in lepton pair production

1 The two-loop approximation

2 Resummation and infrared safe processes

10.2 Transverse gluons in the static limit

1 The magnetic mass

2 Linde's problem

10.3 Soft photon production

10.4 Fermion damping rate

References and further reading

Exercises

A Formulary

B Operator formalism

References

Index