Manifestly covariant canonical quantization of the scalar field and particle localization

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 [Formula: see text], which is the simultaneity surface associated with the observer, whose proper time direction is orthogonal to [Formula: see text]. Position on [Formula: see text] is determined by a 4-vector [Formula: see text]. The corresponding quantum position operator, formed in terms of the operators [Formula: see text], [Formula: see text], that create/annihilate particles on [Formula: see text], has thus well-behaved properties under Lorentz transformations. A generic state is a superposition of the states, created with [Formula: see text], 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.