  In Rindler space, we consider the Feynman Green's functions associated with
either the Fulling-Rindler vacuum or the Minkowski vacuum. In Euclidean field
theory, they becomes respectively the Euclidean Green's functions $G_{\infty}$
and $G_{\2\pi}$, whose we give different suitable forms. In the case of the
massive spin-$\frac{1}{2}$ field, we determine also the Euclidean spinor
Green's function $S_{\infty}$ and $S_{\2\pi}$ in different suitable forms. In
both cases for massless fields in four dimensions, we compute the vacuum
expectation value of the energy-momentum tensor relative to the Rindler
observer.
