  In the present paper the fermion fields, living in the background of
five-dimensional warped brane world models with compact extra dimension, are
thoroughly examined. The Kaluza-Klein decomposition and isolation of the
physical degrees of freedom is performed for those five-dimensional fermion
field Lagrangians, which admit such a decomposition to be performed in a
mathematically consistent way and provide a physically reasonable
four-dimensional effective theory. It is also shown that for the majority of
five-dimensional fermion field Lagrangians there are no (at least rather
obvious) ways to perform the Kaluza-Klein decomposition consistently. Moreover,
in these cases one may expect the appearance of various pathologies in the
four-dimensional effective theory. Among the cases, for which the Kaluza-Klein
decomposition can be performed in a mathematically consistent way, the case,
which reproduces the Standard Model by the zero Kaluza-Klein modes most closely
regardless of the size of the extra dimension, is examined in detail in the
background of the Randall-Sundrum model.
