  The construction of quantum field theory (QFT) of a free massive scalar field
with respect to a general congruence of observers is considered, the splitting
into positive- and negative-frequency modes being defined by diagonalization of
the instantaneous Hamiltonian. The explicit expression for the ultraviolet
asymptotics of the average number of particles created from the vacuum is
found. It is shown that, for a general congruence of observers in the
$D$-dimensional spacetime with $D\geqslant3$, the total number of created
particles diverges in the ultraviolet domain in the regularization removal
limit. This holds even in the Minkowski spacetime. Therefore, in this case, the
quantum evolution is not unitary in the regularization removal limit. It is
proved that not all classically admissible congruences of observers are proper
on a quantum level. Namely, unitarity of QFT with respect to a congruence of
observers is violated when the equal time hypersurfaces of this congruence are
not spacelike, even for a theory with a finite cutoff. The implications of
these results are discussed.
