Defines IR-finite amplitudes M_E that preserve analyticity and unitarity to derive positivity bounds on EFTs including electromagnetism and gravity in D=4.
S-Matrix for massless particles
5 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The traditional $S$-matrix does not exist for theories with massless particles, such as quantum electrodynamics. The difficulty in isolating asymptotic states manifests itself as infrared divergences at each order in perturbation theory. Building on insights from the literature on coherent states and factorization, we construct an $S$-matrix that is free of singularities order-by-order in perturbation theory. Factorization guarantees that the asymptotic evolution in gauge theories is universal, i.e. independent of the hard process. Although the hard $S$-matrix element is computed between well-defined few particle Fock states, dressed/coherent states can be seen to form as intermediate states in the calculation of hard $S$-matrix elements. We present a framework for the perturbative calculation of hard $S$-matrix elements combining Lorentz-covariant Feynman rules for the dressed-state scattering with time-ordered perturbation theory for the asymptotic evolution. With hard cutoffs on the asymptotic Hamiltonian, the cancellation of divergences can be seen explicitly. In dimensional regularization, where the hard cutoffs are replaced by a renormalization scale, the contribution from the asymptotic evolution produces scaleless integrals that vanish. A number of illustrative examples are given in QED, QCD, and $\mathcal{N}=4$ super Yang-Mills theory.
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Faddeev-Kulish dressings correctly encode the memory effect in in and out Fock spaces for massive QED and perturbative quantum gravity, with physical contributions to memory eigenvalues from the dressings.
A universal forward-scattering description in long-range theories makes partial-wave amplitudes well-defined single-scale objects computable order-by-order without spurious IR dependence.
A uniformly moving charge's field is a static Coulomb field in geodesic-centered coordinates, and in AdS the same construction yields a closed-form field with exact antipodal covariance whose null-fringe limits give flat-space antipodal matching.
citing papers explorer
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Positivity with Long-Range Interactions
Defines IR-finite amplitudes M_E that preserve analyticity and unitarity to derive positivity bounds on EFTs including electromagnetism and gravity in D=4.
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Asymptotic charges as detectors and the memory effect in massive QED and perturbative quantum gravity
Faddeev-Kulish dressings correctly encode the memory effect in in and out Fock spaces for massive QED and perturbative quantum gravity, with physical contributions to memory eigenvalues from the dressings.
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Partial-wave unitarity and long-range interactions
A universal forward-scattering description in long-range theories makes partial-wave amplitudes well-defined single-scale objects computable order-by-order without spurious IR dependence.
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Li\'enard--Wiechert fields in AdS and flat-space antipodal matching from geodesic-centered Coulombic data
A uniformly moving charge's field is a static Coulomb field in geodesic-centered coordinates, and in AdS the same construction yields a closed-form field with exact antipodal covariance whose null-fringe limits give flat-space antipodal matching.
- Comments on Symmetry Operators, Asymptotic Charges and Soft Theorems