2003 Prépublication d'Orsay numéro 2003-46 (06/10/2003)



THERMAL QUANTUM FIELDS WITH SPATIALLY CUT-OFF INTERACTIONS IN 1+1 SPACE-TIME DIMENSIONS

GERARD, Christian - Analyse Numérique et E.D.P., Université Paris-Sud, Bât. 425, 91405 Orsay cedex
JAKEL, Christian - Analyse Numérique et E.D.P., Université Paris-Sud, Bât. 425, 91405 Orsay cedex



Mots Clés : Constructive field theory#thermal field theory#KMS states

Classification MSC : 81T08#82B21#82B31#46L55



Resumé :

Abstract :
We construct interacting quantum fields in 1+1 space-time dimensions, representing char\--ged or neutral scalar bosons at positive temperature and zero chemical potential. Our work is based on prior work by Klein and Landau and H\o egh-Krohn. Generalized path space methods are used to add a spatially cut-off interaction to the free system, which is described in the Araki-Woods representation. It is shown that the interacting KMS state is normal w.r.t.\ the Araki-Woods representation. The observable algebra and the modular conjugation of the interacting system are shown to be identical to the ones of the free system and the interacting Liouvillean is described in terms of the free Liouvillean and the interaction.

Contact : christian.gerard@math.u-psud.fr