  We develop an operator description, much like thermofield dynamics, for
quantum field theories on a real time path with an arbitrary parameter
$\sigma\,(0\leq\sigma\leq\beta)$. We point out new features which arise when
$\sigma\neq \frac{\beta}{2}$ in that the Hilbert space develops a natural,
modified inner product different from the standard Dirac inner product. We
construct the Bogoliubov transformation which connects the doubled vacuum state
at zero temperature to the thermal vacuum in this case. We obtain the thermal
Green's function (propagator) for the real massive Klein-Gordon theory as an
expectation value in this thermal vacuum (with a modified inner product). The
factorization of the thermal Green's function follows from this analysis. We
also discuss, in the main text as well as in two appendices, various other
interesting features which arise in such a description.
