  Vacuum polarization of a massive scalar field in the background of a
two-dimensional version of a spinning cosmic string is investigated. It is
shown that when the `radius of the universe' is such that spacetime is globally
hyperbolic the vacuum fluctuations are well behaved, diverging though on the
`chronology horizon'. Naive use of the formulae when spacetime is nonglobally
hyperbolic leads to unphysical results. It is also pointed out that the set of
normal modes used previously in the literature to address the problem gives
rise to two-point functions which do not have a Hadamard form, and therefore
are not physically acceptable. Such normal modes correspond to a locally (but
not globally) Minkowski time, which appears to be at first sight a natural
choice of time to implement quantization.
