# QUARK GLUON PLASMA

## Strange Quark Production

The production rate of strange quarks and antiquarks in a
thermalized quark gluon plasma was calculated during my
PhD thesis supervised by ** J. Zimányi **.
This leading order calculation in the perturbative
QCD showed that the equilibration time of strange
quark production is in the order of a few fm/c and is
dominated by the gg -> ss process
[5,
8,
13,
14] .
This work has been done contemporarily with a similar
work of ** B. Müller ** and ** J.Rafelski **.
In 1990 I returned to this problem again by calculating
the strange quark production rate in a plasma of
massive gluons with Drs
** P.Lévai ** and ** B.Müller **.
If gluons were more massive then two strange quarks also
the g -> ss one gluon decay would contribute
[32] .
According to recent perturbative estimates, however,
this is not the case, so in general the in-medium
production rates are somewhat reduced.

## Gluon Mass

The gluon mass, obtained from the static, long-wavelength limit
of the gluon self-energy characterizes the degree of
interaction in a gluon plasma. It can therefore be used
for parametrizing the non-ideal equation of state.
Furthermore, in the framework of variational approach
to the QCD at low and high temperatures the gluon mass
can be used as an order parameter signalling a first
order phase transition of the pure glue.
In the years 1987 - 1989 I worked out such a variational
model of QCD which describes the most important
phenomenological aspects from the gluon condensate
to heavy quark confinement using a single scale
parameter, the gluon mass, only
[5,
25,
27,
29,
31,
35].

These investigations are also reviewed in my habilitation
thesis.
Further work related to the confinement phenomenology
can be found in
[23,
28].

## Screening

In a gluon plasma a thermal screening mass, which
modifies the Coulomb potential between heavy charges to a
Yukawa type one, can be calculated relatively easily
in analogy to the calculation of the Debye mass in
a plasma of electric charges.
With Drs ** B. Müller ** and
** X. N. Wang ** we estimated the
Debye mass in an anisotrop parton medium; the polarisation
tensor looses its sphericity in this case.
A slight difference between longitudinal (paralell moving
test charge) and transverse (orthogonally moving test charge)
Debye masses has been found
[36] .

## Magnetic Screening

Unlike the Debye mass a static, long wavelength
magnetic screening cannot be described perturbatively.
With ** B. Müller ** we estimated this quantity by
stabilizing solitons carrying a magnetic monopole
charge in a semiclassical calculation due to a
scale invariance breaking energy term.
The density of such configurations was then obtained
in a saddle point approximation and finally an
integration over the artificially induced scale
completed the calculation. We obtained a static
magnetic mass of ### m = 0.255 g ² T

for SU(2) [37] .

## Chaos

My investigations about the chaotic dynamics
of the classical Hamiltonian lattice gauge theory
started in 1991 when together with
** B.Müller, A.Trayanov ** and ** C.Gong **
at the Duke University
we carried out a series of calculations for SU(2),
U(1) and SU(3) systems.
The scaling of the leading Lyapunov exponent
with the total energy of the initial configuration
and for small lattices the complete Lyapunov
spectrum has been obtained
[6,
40].
A review of the role of chaos in gauge theory
can be found in our recently published book
[7]
(co-authors ** S. Matinyan ** and ** B. Müller **).
Further developments are published in
[43,
44,
45] .

Investigations of the effect of static charges
[46]
and Higgs fields
[47]
followed. Recently we study the Lyapunov exponent
for lattice configurations generated by quantum
Monte Carlo simulations (collaborator** H. Markum **).

## A sample configuration on the lattice

This figure shows a sample configuration on a
10 x 10 x 10 lattice. The 1-Tr(Up) values are
averaged for all four plaquettes attached on a
given link. These are color coded in the interval
(0,2).

The diagram shows the distribution of the plaquette
energies at a finite temperature.