Abstract
We investigate the memory effects associated with the kicks of particles. Recently, the equivalence between the memory effect and soft theorem has been established. By computing the memory effect from the radiation solutions, we explicitly confirm that, in addition to the leading piece, the subleading and subsubleading soft theorems are equivalent to the subleading and subsubleading memory effects, respectively. It is known that the memory effects can be probed by the displacements or kicks of the test particles. We point out that the these memory effects are also probed by the permanent change of the direction of the spin. We also show that the axion memory effect, recently proposed by the current authors, can be detected as the change of the spin of the test particle. We discuss that if we consider the magnetic monopole as an external particle, the parity-odd electromagnetic memory appears.
Highlights
Theoretically interesting because it has a strong connection to the notion such as the soft graviton theorem and asymptotic symmetry [13,14,15,16,17,18,19]
In addition to the leading order, we look at the subleading and the subsubleading memories characterized by the δ(u) and δ (u) terms in the classical radiation, and show that they are related to the soft factors in the subleading and subsubleading soft theorems
We have found that the classical radiation fields up to subsubleading order can be correctly reproduced the soft factors which are consistent with known soft theorems
Summary
We consider the electromagnetic potential induced from kicks of charged particles, and see that it leads to the electromagnetic memory. Our justification to consider the trajectory (2.1) and (2.2) relies on the leading and the subleading soft theorems in QED These soft theorems state that the soft factors are determined by the initial momenta and angular momenta of particles and do not depend on the details of the scattering. For the radiation by the kick (2.6), the leading and subleading memories are related to the coefficient of the step function Θ(u) and the delta function δ(u), respectively.. For the radiation by the kick (2.6), the leading and subleading memories are related to the coefficient of the step function Θ(u) and the delta function δ(u), respectively.8
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