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arxiv: 1804.03404 · v2 · pith:TF5GGFCFnew · submitted 2018-04-10 · ✦ hep-th · quant-ph

Manifestly Covariant Canonical Quantization of the Scalar Field and Particle Localization

classification ✦ hep-th quant-ph
keywords covariantsigmafieldparticlecanonicaldaggergenericlocalization
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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.

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