Classicized dynamics and initial conditions in field theories with fakeons

TL;DR

This work clarifies how classical dynamics emerges in theories with fakeons by introducing classicization, a process that integrates out purely virtual particles to produce nonlocal but DOF-consistent equations of motion. The authors establish that the nonlocal corrections do not increase the number of initial conditions because the solution space of the fakeon system is a finite-dimensional subspace of the parent higher-derivative theory, and the extra degrees of freedom are removed by rendering them purely virtual. They demonstrate this both with explicit solvable one-dimensional models and with a general proof that relies on viewing the fakeon inversion as a limit of a more generic prescription. The results provide a coherent classical limit for fakeon theories and connect to Dirac’s method for removing runaway solutions, with potential implications for quantum gravity, cosmology, and nonlocal phenomenology, while maintaining consistency with unitarity and renormalizability at the quantum level.

Abstract

Theories with purely virtual particles (fakeons) do not possess a classical action in the strict sense, but rather a "classicized" one, obtained by integrating out the fake particles at tree level. Although this procedure generates nonlocal interactions, we show that the resulting classicized equations of motion are not burdened with the need to specify infinitely many initial conditions. The reason is the inherent link between the fakeonic system and the parent higher-derivative local system: the solution space of the former is an appropriate subspace of solutions of the latter. A somewhat unexpected proviso is that, in order to avoid overcounting, the fakeon prescription must be obtained as a limit or special case of a more generic prescription. Ultimately, the number of degrees of freedom matches physical expectations, the extra ones (ghosts or otherwise) being removed by rendering them purely virtual. We illustrate the counting in simple linear solvable models and provide the general proof. Along similar lines, we analyze Dirac's removal of runaway solutions in classical electrodynamics.