  In flat spacetime, two inequivalent vacuum states which arise rather
naturally are the Rindler vacuum (R) and the Minkowski vacuum (M). We disuss
several aspects of the Rindler vacuum, concentrating on the propagator and
Schwinger (heat) kernel defined using R, both in the Lorentzian and Euclidean
sectors. We start by exploring an intriguing result due to Candelas and Raine ,
viz., that $G_{R}$, the Feynman propagator corresponding to R, can be expressed
as a curious integral transform of $G_{M}$, the Feynman propagator in M. We
show that, this relation actually follows from the well known result that,
$G_{M}$ can be written as a periodic sum of $G_{R}$, in the Rindler time
$\tau$, with the period $2\pi i$. We further show that, the integral transform
result holds for a wide class of pairs of bi-scalars $(F_{M},F_{R})$, provided
$F_{M}$ can be represented as a periodic sum of $F_{R}$ with period $2\pi i$.
We provide an explicit procedure to retrieve $F_{R}$ from its periodic sum
$F_{M}$, for a wide class of functions. An example of particular interest is
the pair of Schwinger kernels $(K_{M},K_{R})$, corresponding to the Minkowski
and the Rindler vacua. We obtain explicit expression for $K_{R}$ and clarify
several conceptual and technical issues related to these biscalars both in the
Euclidean and Lorentzian sector. In particular we address the issue of
retrieving the information contained in all the four wedges of the Rindler
frame in the Lorentzian sector, starting from the Euclidean Rindler (polar)
coordinates. This is possible but require four different types of analytic
continuations, based on one unifying principle. Our procedure allows
generalisation of these results to any (bifurcate Killing) horizon in curved
spacetime.
