Abstract The quantum theory of free Dirac's massive fermions is reconstructed around the new conserved spin operator and its corresponding position one proposed initially by Pryce long time ago and re-defined recently with the help of a new spin symmetry and suitable spectral representations. [I. I. Cot\u aescu, Eur. Phys. J. C (2022) 82:1073]. This approach is generalized here associating to any integral operator in configuration representation a pair of integral operators acting directly on particle and antiparticle wave spinors in momentum representation without affecting the mode spinors. This framework allows an effective quantization procedure giving a large set of one-particle operators with physical meaning as the spin and orbital parts of the isometry generators, the Pauli-Lubanski and position operators or other spin-type operators proposed so far. A special attention is paid to the operators which mix the particle and antiparticle sectors whose off-diagonal associated operators have oscillating terms producing Zitterbevegung. The principal operators of this type including the usual coordinate operator are derived here for the first time. As an application, it is shown that an apparatus measuring these new observables may prepare and detect one-particle wave-packets moving uniformly without Zitterbewegung or spin dynamics, spreading in time normally as any other relativistic even non-relativistic wave-packet. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.