# Local Thermal Equilibrium and KMS states in Curved Spacetime

November 02, 2012

On the example of a free massless and conformally coupled scalar field, it is
argued that in quantum field theory in curved spacetimes with time-like Killing
field, the corresponding KMS states (generalized Gibbs ensembles) at parameter
$\beta>0$ need not possess a definite temperature in the sense of the zeroth law.
In fact, these states, although passive in the sense of the second law, are not
always in local thermal equilibrium (LTE). A criterion characterizing LTE
states with sharp local temperature is discussed. Moreover, a proposal is made
for fixing the renormalization freedom of composite fields which serve as
"thermal observables" and a new definition of the thermal energy of LTE states
is introduced. Based on these results a general relation between the local
temperature and the parameter \beta is established for KMS states in (Anti) de
Sitter spacetime.

Keywords:

local thermal equilibrium, QFT on curved spacetimes