Effective descriptions of localization in a proper-time parametrized framework

Abstract: Although the quantization of relativistic systems in a proper-time framework gives new insights concerning the understanding of the so-called localization problem, classical observers cannot be treated as quantum comoving frames and real measurement are typically conceived using an external parameter related to a classical frame. Here, the connection between the proper-time formalism and usual descriptions parametrized by classical observers is obtained by defining a restriction operation that mixes contributions of different values of proper-time. Such a restriction procedure allows us to retrieve the concepts of Newton-Wigner position and Kijowski time of detection in an effective fashion, opening the possibility to interpret the related causalities issues as an apparent phenomena resulting from the time uncertainty that is inherent to every physically acceptable single-particle quantum state.