Asymptotic U(1) charges at spatial infinity

Abstract

Large gauge symmetries in Minkowski spacetime are often studied in two distinct regimes: either at asymptotic (past or future) times or at spatial infinity. By working in harmonic gauge, we provide a unified description of large gauge symmetries (and their associated charges) that applies to both regimes. At spatial infinity the charges are conserved and interpolate between those defined at the asymptotic past and future. This explains the equality of asymptotic past and future charges, as recently proposed in connection with Weinberg’s soft photon theorem.

Source and response soft charges for Maxwell theory on AdSd

“…The phase space of all superpositions of boosted electric charges consists of all functions ψ(ρ, x µ ) satisfying conditions (3.7). Finally, note that near the origin, ρ ≪ ℓ, the behavior is ψ ∝ ρ 3−d which matches flat space solutions [22,26]. Near the boundary, however, the behavior is weaker ψ ∝ ρ 2−d .…”

“…We also discuss how the AdS d isometry charges act on our soft mode phase space. In section 7, we show how our results on AdS d and those studied in the literature for Maxwell theory on flat space [19][20][21][22][23][24][25][26][27] could be related to each other through an AdS (large radius) flat space limit. In particular, we show that only the source boundary gauge transformations and the associated soft charges survive the limit and the response charges become subdominant and do not appear in the limit.…”

Generalized asymptotics for gauge fields

“…Specifically, with finite energy initial data, corresponding to an EM field that disperses to infinity, we might expect regular evolution. This seems at odds with claims [5][6][7][8]16] of singular behavior at I + .…”

“…For u > −R 2 , the integrals with integrands given by (7) are cut off at r = R 2 . This means that in the bounds (16), (17), u is replaced by R 2 for u > −R 2 . 4 There is also a contribution from the initial data in the region R 1 < r < R 2 .…”

“…One expects this solution to be finite, and finiteness of the asymptotic behavior is confirmed by investigating bounds on this solution. Arguments for singular evolution of non-antipodal data [5][6][7][8]16] are reexamined, and found to not imply singularities in the usual electromagnetic fields. The question of the symplectic form is also briefly considered, and it is argued that the symplectic form has finite behavior.…”