ECT* Doctoral Training Programme 2006:
Computational Techniques in Strongly Interacting Systems

Quantum Field Theory out of Equilibrium

I. What is non-equilibrium field theory? Why non-equilibrium field theory?
• thermal equilibrium: imaginary time/real time, KMS condition
• path integral: non-equilibrium system, Schwinger-Keldysh contour
• applications: (end of) inflation, heavy ion collisions, quark-gluon plasma

II. Linear response
• retarded Green's functions
• spectral functions

III. Spectral functions
• (quasi)particles
• diagrammatic example: one-loop gauge boson
• lattice approach: Maximal Entropy Method

IV. Transport coefficients
• hydrodynamics
• Kubo relations
• diagrammatic approach: large Nf gauge theories
• lattice approach

V. Far from equilibrium
• requirements
• two-particle irreducible (2PI) effective action
• causal equations of motion
• 2PI-1/N expansion
• numerical solution and examples
• classical statistical field theory
• accuracy of the 2PI-1/N expansion
• beyond 2PI: stochastic quantization and non-equilibrium quantum fields