  We demonstrate how to obtain explicitly the propagators for quantum fields
residing in curved space-time using the heat kernel for which a new
construction procedure exists. Propagators are determined for the case of
Rindler, Friedman-Robertson-Walker, Schwarzschild and general conformally flat
metrics, both for scalar, Dirac and Yang-Mills fields. The calculations are
based on an improved formula for the heat kernel in a general curved space. All
the calculations are done in $d=4$ dimensions for concreteness, but are easily
generalizable to arbitrary $d$. The new method advocated here does not assume
that the fields are massive, nor is it based on an aymptotic expansion as such.
  Whenever possible, the results are compared to that of other authors.
