H.J. Borchers, J. Yngvason
Modular groups of Quantum Fields in Thermal States
(52K, Tex, figures in Postscript)

ABSTRACT.  For a quantum field in a thermal equilibrium state we discuss the 
group generated by time translations and the modular action associated 
with an algebra invariant under half-sided translations.  The modular 
flows associated with the algebras of the forward light cone and a 
space-like wedge admit a simple geometric description in two 
dimensional models that factorize in light-cone coordinates.  At large 
distances from the domain boundary compared to the inverse temperature 
the flow pattern is essentially the same as time translations, whereas 
the zero temperature results are approximately reproduced close to the 
edge of the wedge and the apex of the cone.  Associated with each 
domain there is also a one parameter group with a positive generator, 
for which the thermal state is a ground state.  Formally, this may be 
regarded as a certain converse of the Unruh-effect.