To make clearer the relation examined in a previous paper between Chitre and Hartle's path-integral quantization procedure and our canonical one for a massive scalar field in a special isotropic universe, various propagators such as the 4-dimensional commutation function, the elementary solution and the associated Feynman propagator are explicitly determined. Owing to the determination, there arises a new changing procedure superior to the previous one from the isotropic expanding universe to the Minkowski space-time. Thus it is shown without any ambiguity that both the path-integral quantization procedure and our canonical one leading to the same pair-creation of particles as Chitre and Hartle's cannot recover the usual theory for a free field in the limit when the cosmic expansion disappears. (Notice, however, that our quantization procedure permits another case which can recover the Minkowski theory for a free field in the above limit , while it gives rise to no pair-creation.) Propagators for a massless scalar field are also dealt with in connection with the problem of conformal anomaly arising in the vacuum expectation value of the stress-energy tensor for our quantized scalar field, which is common to any quantized field in a curved space-time.