Abstract
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 Σ, which is the simultaneity surface associated with the observer, whose proper time direction is orthogonal to Σ. Position on Σ is determined by a 4-vector x^μ. The corresponding quantum position operator, formed in terms of the operators a^† (x), a(x), that create/annihilate particles on Σ, has thus well behaved properties under Lorentz transformations. A generic state is a superposition of the states, created with a^† (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.