Asymptotic conservation law with Feynman boundary condition

Recently it was shown that classical electromagnetism admits new asymptotic conservation laws [, New asymptotic conservation laws for electromagnetism, J. High Energy Phys. 02 (2021) 082.]. In this paper we derive the analog of the first of these asymptotic conservation laws upon the imposing Feynman boundary condition on the radiative field. We also show that the Feynman solution at O(e3) contains purely imaginary modes falling off as ... which are absent in the retarded solution. The logu mode has also appeared [ and , Loop corrected soft photon theorem as a Ward identity, J. High Energy Phys. 10 (2019) 287; , Ward identity for loop level soft photon theorem for massless QED coupled to gravity, J. High Energy Phys. 10 (2020) 110.] and violates the Ashtekar-Struebel falloffs for the radiative field [ and , Symplectic geometry of radiative modes and conserved quantities at null infinity, Proc. R. Soc. A 376, 585 (1981).]. We expect that new ... modes would appear in the Feynman solution at order O(e2m+1). Thus, all the other modes are expected to preserve the Ashtekar-Struebel falloffs.