 
Summary: arXiv:hepph/9809339
v1
11
Sep
1998
The Classical Approximation for RealTime Scalar Field Theory at Finite
Temperature
Gert Aarts
Institute for Theoretical Physics, Utrecht University
Princetonplein 5, 3508 TA Utrecht, the Netherlands
aarts@phys.uu.nl
(September 1, 1998)
The use of classical thermal eld to approximate realtime quantum thermal eld theory is
discussed. For a 4 theory, it is shown that the classical RayleighJeans divergence can be canceled
with the appropriate counterterms, and a comparison is made between the classical and quantum
perturbative expansion. It is explained why Hard Thermal Loops prevent the same method to work
for gauge theories.
I. INTRODUCTION
Realtime dynamics of quantum elds plays an im
portant role in the early universe (baryogenesis, in
a
