 
Summary: ELSEVIER Nuclear Physics B 511 (1998) 451478
Classical approximation for timedependent
quantum field theory: Diagrammatic analysis for
hot scalar fields
Gert Aarts a,l Jan Smit a,b,2
a Institute for Theoretical Physics, Utrecht University, Princetonplein 5, 3508 TA Utrecht, The Netherlands
b Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam,
The Netherlands
Received 16 July 1997;accepted 23 October 1997
Abstract
We study timedependent correlation functions in hot quantum and classical field theory for the
,~b4 case. We set up the classical analogue of thermal field theory and make a direct compar
ison between the quantum and classical diagrams. A restriction to timeindependent correlation
functions gives the connection with conventional dimensional reduction. If the parameters in the
classical theory are chosen according to the dimensional reduction matching relations, the classical
expressions are cutoff independent and they approximate the quantum expressions, provided that
the external momenta and frequencies are small with respect to the temperature. (~) 1998 Elsevier
Science B.V.
PACS: ll.10.Wx; ll.10.Gh; ll.15.Kc
Keywords: Realtime quantum field theory at finitetemperature; Classical approximation
