1202.0732 (H. T. Cho et al.)

Stress-energy Tensor Correlators in N-dim Hot Flat Spaces via the
Generalized Zeta-Function Method    [PDF]

H. T. Cho, B. L. Hu

We calculate the expectation values of the stress-energy bitensor defined at
two different spacetime points $x, x'$ of a massless, minimally coupled scalar
field with respect to a quantum state at finite temperature $T$ in a flat
$N$-dimensional spacetime by means of the generalized zeta-function method.
These correlators, also known as the noise kernels, give the fluctuations of
energy and momentum density of a quantum field which are essential for the
investigation of the physical effects of negative energy density in certain
spacetimes or quantum states. They also act as the sources of the
Einstein-Langevin equations in stochastic gravity which one can solve for the
dynamics of metric fluctuations as in spacetime foams. In terms of
constitutions these correlators are one rung above (in the sense of the
correlation -- BBGKY or Schwinger-Dyson -- hierarchies) the mean (vacuum and
thermal expectation) values which drive the semiclassical Einstein equation in
semiclassical gravity. The low and the high temperature expansions of these
correlators are also given here: At low temperatures, the leading order
temperature dependence goes like $T^{N}$ while at high temperatures they have a
$T^{2}$ dependence with the subleading terms exponentially suppressed by
$e^{-T}$. We also discuss the singular behaviors of the correlators in the
$x'\rightarrow x$ coincident limit as was done before for massless conformal
quantum fields.

View original: http://arxiv.org/abs/1202.0732