Euclidean scalar and spinor Green's functions in Rindler space

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 $G_{\mathrm{\infty }}$ and $G_{\text{2}\pi }$, 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 $S_{\mathrm{\infty }}$ and $S_{\text{2}\pi }$ 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.