Abstract
We apply the recently developed formalism by Kosower, Maybee and O’Connell (KMOC) [12] to analyse the soft electromagnetic and soft gravitational radiation emitted by particles without spin in D ≥ 4 dimensions. We use this formalism in conjunction with quantum soft theorems to derive radiative electro-magnetic and gravitational fields in low frequency expansion and upto next to leading order in the coupling. We show that in all dimensions, the classical limit of sub-leading soft (photon and graviton) theorems is consistent with the classical soft theorems proved by Sen et al. in a series of papers. In particular in [11] Saha, Sahoo and Sen proved classical soft theorems for electro-magnetic and gravitational radiation in D = 4 dimensions. For the class of scattering processes that can be analyzed using KMOC formalism, we show that the classical limit of quantum soft theorems is consistent with the D = 4 classical soft theorems, paving the way for their proof from scattering amplitudes.
Highlights
Was shown that extremizing the probability distribution of emitted soft quanta in a given frequency bin is tantamount to taking the classical limit and results in classical radiation arranged in soft frequency expansion
For the class of scattering processes that can be analyzed using KMOC formalism, we show that the classical limit of quantum soft theorems is consistent with the D = 4 classical soft theorems, paving the way for their proof from scattering amplitudes
The radiative field at long distances is proportional to the “classical limit” of a single soft factor where momentum and angular momentum operators in quantum theory are replaced by their classical counter-parts
Summary
We review the classical soft theorems derived by Sen and his collaborators in a series of papers. In the large impact parameter regime, these terms are sub dominant and upto sub-leading order in the frequency, the radiative gauge field is universal, depending only on the asymptotic linear momentum and angular momentum of scattering particles. The classical soft graviton theorems at sub-leading order are statements regarding universality of low frequency gravitational field in the radiation regime. In the more standard approach to classical radiation (see [31] and references therein), one starts with an initial configuration of scattering particles with certain boundary conditions and computes outgoing radiation in the far future using equations of motion Seen from this perspective, the soft factors are really “re-summed results” obtained from classical perturbation theory once we know the exact final momentum of a particle in terms of initial momenta. When we compute soft radiation perturbatively in the coupling, a necessary condition for consistency with the soft factor is that the radiation at any perturbative order is consistent with classical soft factor
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