Daniel F. Litim
Institut f. Theoretische
Physik,
Philosophenweg 16,
D - 69120 Heidelberg.
I report about some recent results obtained in collaboration with Cristina Manuel (see also her seminar at this workshop). The main references are:
1. General approach
The aim is to systematically derive effective transport equations describing
(non-Abelian) plasmas built out of quarks and gluons. A kinetic theory
for non-Abelian plasmas is of particular interest for the physics of the
early universe (like the baryon number violation rate), and possibly for
the central region of heavy ion collisions. In either case a formalism
is required able to cover both close-to-equlibrium and out-of-equilibrium
situations.
Our approach is based on a classical transport theory for coloured point particles obeying classical equations of motions, the Wong equations. These particles are coupled self-consistently to the Yang-Mills field. This leads immediately to a Boltzmann equation for the (microscopic) one-particle distribution function.
The new ingredience consists in taking the (Gibbs) ensemble average in phase space over the particles in order to obtain the effective (macroscopic) Boltzmann and Yang-Mills equations for the mean fields. At the same time, dynamical equations for the fluctuations about the mean values are obtained. This step has important conceptual implications, as the mean field equations, due to the intrinsic non-linearities, are not closed by themselves, but coupled to the statistical fluctuations about the mean fields. It appears that collision integrals for the mean fields are identified as correlators of flucutations, which can be seen as a derivation of collision integrals for Boltzmann equations. The coupled set of dynamical equations should be enough to study all transport phenomena occuring in the plasma. Most importantly, these equations do not rely on a close-to-equilibrium scenario.
2. The hot quark-gluon plasma close to equilibrium
Some simplifying approximations can be used when the approach is applied
to a hot non-Abelian plasma close to equilibrium. In an expansion to leading
order in the gauge coupling at logarithmic accuracy, higher order
correlators of fluctuations beyond quadratic order are suppressed and we
recover the Boltzmann-Langevin equation first derived by Bodeker (see his
seminar at this workshop). This includes both a derivation of
the (linearized) collision integral and of the source for stochastic noise.
3. Collision integral vs. noise and the fluctuation-dissipation theorem
In hep-ph/9906210,
the source for stochastic noise has been derived directly form the effective
dynamical equations, and ultimately from the Gibbs ensemble average. One
might wonder whether this noise source is consistent with the fluctuation-dissipation
theorem (FDT), which, in the close to equilibrium case, links the dissipative
processes in the plasma to the underlying fluctuations. And indeed, under
the assumption that the (linearized) dissipative term (i.e. the collision
integral) is known, and assuming the FDT to hold, it is possible to derive
the related noise term phenomenologically, hep-ph/9910348.
The resulting noise source coincides with our previous result, which
establishes that the above formalism ,and in particular Bodeker's effective
theory, is consistent with the FDT.
Daniel F. Litim
D.Litim@thphys.uni-heidelberg.de