  We show that an analogue of the (four dimensional) image sum method can be
used to reproduce the results, due to Krasnikov, that for the model of a real
massless scalar field on the initial globally hyperbolic region IGH of
two-dimensional Misner space there exist two-particle and thermal Hadamard
states (built on the conformal vacuum) such that the (expectation value of the
renormalised) stress-energy tensor in these states vanishes on IGH. However, we
shall prove that the conclusions of a general theorem by Kay, Radzikowski and
Wald still apply for these states. That is, in any of these states, for any
point b on the Cauchy horizon and any neighbourhood N of b, there exists at
least one pair of non-null related points (x,x'), with x and x' in the
intersection of IGH with N, such that (a suitably differentiated form of) its
two-point function is singular. (We prove this by showing that the two-point
functions of these states share the same singularities as the conformal vacuum
on which they are built.) In other words, the stress-energy tensor in any of
these states is necessarily ill-defined on the Cauchy horizon.
