  Particle localization within quantum field theory is revisited. Canonical
quantization of a free scalar field theory is performed in a manifestly Lorentz
covariant way with respect to an arbitrary 3-surface $\Sigma$, which is the
simultaneity surface associated with the observer, whose proper time direction
is orthogonal to $\Sigma$. Position on $\Sigma$ is determined by a 4-vector
${\bar x}^\mu$. The corresponding quantum position operator, formed in terms of
the operators $a^\dagger ({\bar x})$, $a({\bar x})$, that create/annihilate
particles on $\Sigma$, has thus well behaved properties under Lorentz
transformations. A generic state is a superposition of the states, created with
$a^\dagger ({\bar x})$, the superposition coefficients forming multiparticle
wave packet profiles---wave functions, including a single particle wave
function that satisfies the covariant generalization of the Foldy equation. The
covariant center of mass operator is introduced and its expectation values in a
generic multiparticle state calculated.
