Infrared Finite Scattering Theory in Quantum Field Theory and Quantum Gravity
arXiv:2203.14334 · doi:10.1103/PhysRevD.106.066005
Abstract
Infrared (IR) divergences arise in scattering theory with massless fields and are manifestations of the memory effect. There is nothing singular about states with memory, but they do not lie in the standard Fock space. IR divergences are artifacts of trying to represent states with memory in the standard Fock space. For collider physics, one can impose an IR cutoff and calculate inclusive quantities. But, this approach cannot treat memory as a quantum observable and is highly unsatisfactory if one views the S-matrix as fundamental in QFT and quantum gravity, since the S-matrix is undefined. For a well-defined S-matrix, it is necessary to define in/out Hilbert spaces with memory. Such a construction was given by Faddeev and Kulish (FK) for QED. Their construction "dresses" momentum states of the charged particles by pairing them with memory states of the electromagnetic field to produce states of vanishing large gauge charges at spatial infinity. However, in massless QED, due to collinear divergences, the "dressing" has an infinite energy flux so these states are unphysical. In Yang-Mills theory the "soft particles" used for dressing also contribute to the current flux, invalidating the FK procedure. In quantum gravity, the analogous FK construction would attempt to produce a Hilbert space of eigenstates of supertranslation charges at spatial infinity. However, we prove that there are no eigenstates of supertranslation charges except the vacuum. Thus, the FK construction fails in quantum gravity. We investigate some alternatives to FK constructions but find that these also do not work. We believe that to treat scattering at a fundamental level in quantum gravity - as well as in massless QED and YM theory - it is necessary to take an algebraic viewpoint rather than shoehorn the in/out states into some fixed Hilbert space. We outline the framework of such an IR finite scattering theory.
arXiv commentv3: minor edits and updated references, as appears in PRD v2: updated references v1: 82 pages + references, 1 figure (shortened abstract; full abstract in paper)
References in corpus (38)
- Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
- Soft Hair on Black Holes
- On BMS Invariance of Gravitational Scattering
- A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
- Quantum fields in curved spacetime
- An electromagnetic analog of gravitational wave memory
- Infrared Divergences in QED, Revisited
- A perturbative and gauge invariant treatment of gravitational wave memory
- The Holographic Nature of Null Infinity
- Collinear and Soft Divergences in Perturbative Quantum Gravity
- BMS Supertranslations and Memory in Four and Higher Dimensions
- Null infinity, the BMS group and infrared issues
- The BMS4 algebra at spatial infinity
- Asymptotic charges at spatial infinity
- Asymptotic symmetries of electromagnetism at spatial infinity
- Large Gauge Symmetries and Asymptotic States in QED
- The Asymptotic Behavior of Massless Fields and the Memory Effect
- BMS Supertranslation Symmetry Implies Faddeev-Kulish Amplitudes
- Hamiltonian structure and asymptotic symmetries of the Einstein-Maxwell system at spatial infinity
- An -Matrix for Massless Particles
- Equivalence of the (generalised) Hadamard and microlocal spectrum condition for (generalised) free fields in curved spacetime
- Infraparticle Scattering States in Non-Relativistic QED: I. The Bloch-Nordsieck Paradigm
- Uniqueness theorem for BMS-invariant states of scalar QFT on the null boundary of asymptotically flat spacetimes and bulk-boundary observable algebra correspondence
- Conservation of asymptotic charges from past to future null infinity: Supermomentum in general relativity
- Infraparticle Scattering States in Non-Relativistic QED: II. Mass Shell Properties
- Null to time-like infinity Green's functions for asymptotic symmetries in Minkowski spacetime
- Conservation of asymptotic charges from past to future null infinity: Lorentz charges in general relativity
- Dressed infrared quantum information
- The Wald-Zoupas prescription for asymptotic charges at null infinity in general relativity
- Conservation of asymptotic charges from past to future null infinity: Maxwell fields
- From Faddeev-Kulish to LSZ. Towards a non-perturbative description of colliding electrons
- Asymptotic Charges Cannot Be Measured in Finite Time
- Semidirect product of CCR and CAR algebras and asymptotic states in quantum electrodynamics
- Gravitational Memory and Compact Extra Dimensions
- Asymptotic Dynamics in Perturbative Quantum Gravity and BMS Supertranslations
- Angular momentum at null infinity in Einstein-Maxwell theory
- Infrared problem in perturbative quantum field theory
- Generalized coherent states in QCD from asymptotic symmetries