The Infraparticle Edge

Research Question and Approach

This paper addresses the long-standing problem of the charged-particle spectral edge in QED, where the presence of arbitrarily soft photons prevents the existence of an isolated mass shell. Instead of a simple delta-function peak at the mass threshold, the charged sector exhibits a continuous spectral edge. The author uses an open-quantum-system framework, where the hard charged particle is the system and the unresolved soft photons constitute the environment. By defining a quantum instrument for soft QED, the author projects this instrument into two observables: the reduced hard-sector channel (which governs decoherence) and the inclusive energy distribution (which governs the spectral edge).

The author demonstrates that the spectral edge is a direct consequence of the unresolved photon environment. By calculating the energy marginal of the soft-photon configuration, the paper derives the inclusive spectral measure, finding that it follows a power law of the form (s - m^2)^(-1 + η_h), where η_h is the response coefficient of the unresolved photon sector. This result confirms that the infraparticle edge is a massive threshold with a scale-free local profile. Furthermore, the paper establishes a clear distinction between the dephasing exponent (governing the distinguishability of hard alternatives) and the edge exponent (governing the spectral endpoint), both of which are derived from the same underlying soft-photon kernel.

This work provides a unified, rigorous derivation of the infraparticle edge that bridges the gap between soft-photon resummation and open-quantum-system dynamics. By classifying infrared energy marginals, the paper clarifies how the atomic weight of a stable particle is transferred into the continuum as the infrared resolution limit is removed. This framework offers a robust way to understand how environmental interactions—specifically soft-photon emission—fundamentally alter the spectral properties of charged particles, providing a clear physical interpretation of the branch point at the mass threshold.