Infrared sectors and infraparticles
For a specified charged model, construct infrared-finite scattering predictions for stated inclusive observables and asymptotic charge sectors, prove the applicable completeness statement, and control collinear singularities where massless charged particles ar
Problem statement
For a specified charged model, construct infrared-finite scattering predictions for stated inclusive observables and asymptotic charge sectors, prove the applicable completeness statement, and control collinear singularities where massless charged particles are included.
Lean 4
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Background
In QED a charged particle is inevitably accompanied by a cloud of soft photons; it is an 'infraparticle' with no sharp mass and does not sit in a standard Wigner irreducible representation of the Poincaré group. Naive scattering amplitudes are infrared-divergent, and the usual Fock-space asymptotic states do not exist for charged particles.
What is known: Several partial frameworks address this. Bloch–Nordsieck and the Faddeev–Kulish construction dress charged states with coherent clouds of soft photons to yield IR-finite S-matrix elements. Algebraically, Buchholz and collaborators developed the theory of superselection sectors, the Gauss-law charge, and the breaking of Lorentz symmetry in charged sectors, characterizing infraparticles rigorously. More recently the connection to asymptotic symmetries and soft theorems (Strominger et al.) and to the memory effect has reorganized the subject, linking soft photons to large gauge transformations.
Published progress: Prabhu–Satishchandran (2024) develop an algebraic infrared-finite scattering construction using generalized asymptotic states and superscattering, with soft theorems. This advances the formalism without providing a nonperturbative construction of four-dimensional QED or removing every collinear difficulty.
The frontier is model-specific control: relate the algebraic asymptotic data to finite-resolution detector probabilities, state the sectors on which completeness holds, and prove existence/error bounds under the chosen infrared and collinear assumptions. A uniquely preferred notation or universal agreement between formalisms is not the success criterion. Related: QF3, QF6.
Progress & source assessment
Source catalogue review: 4 September 2026. Improved indicates partial progress, including qualified preprint claims.
- [1]Buchholz, 'Gauss' law and the infraparticle problem', Phys. Lett. B174 (1986) link
- [2]Strominger, 'Lectures on the Infrared Structure of Gravity and Gauge Theory' (Princeton, 2018) link
- [3]Prabhu & Satishchandran, 'Infrared finite scattering theory: Amplitudes and soft theorems', PRD 110, 085022 (2024) link
Recorded progress
Add yours →Nothing recorded yet. A pointer to a paper the entry is missing counts.
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Discussion
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