Zeno-Constrained Formation of Relativistic Mass Shells

We study an extension of the quantum linear Boltzmann equation describing irreversible momentum space dynamics of an open quantum system under strong continuous monitoring. The monitored observable is taken to be a quadratic form in an extended, purely Euclidean four-dimensional momentum space, without assuming any fixed signature at the microscopic level. In the resulting quantum Zeno regime, rapid suppression of off-constraint excursions allows for an adiabatic elimination of fast degrees of freedom. Using a Schur complement construction, the induced second-order corrections give rise to an effective flow of the monitored quadratic form under temporal coarse graining. Under mild isotropy assumptions on the underlying momentum-mixing dynamics and an appropriate calibration condition, this flow approaches an infrared fixed point characterized by a quadratic form of Lorentzian signature. The corresponding null set defines a mass shell-like constraint surface that governs the long-time Zeno-projected dynamics and whose isometry group matches the kinematic structure of Lorentz transformations at the effective level. Familiar relativistic features, including Maxwell–Jüttner type stationary distributions, arise at the level of the effective infrared description as consequences of this fixed point within the extended quantum Boltzmann framework.