Asymptotic conservation law with Feynman boundary condition

Abstract

Recently it was shown that classical electromagnetism admits new asymptotic conservation laws \cite{2007.03627}. In this paper we derive the analogue of the first of these asymptotic conservation laws upon imposing Feynman boundary condition on the radiative field. We also show that the Feynman solution at $\mathcal{O}(e^3)$ contains purely imaginary modes falling off as $\{\frac{\log u}{u^{n}r},n\ge 0\}$ which are absent in the retarded solution. The $\log u$ mode has also appeared in \cite{1903.09133,1912.10229} and violates the Ashtekar-Struebel fall offs for the radiative field\cite{AS}. We expect that new $\frac{(\log u{)}^m}{u^{m}r}$-modes would appear in the Feynman solution at order $\mathcal{O}(e^{2m+1})$. Thus, all the other modes are expected to preserve the Ashtekar-Struebel fall offs.

arXiv commentMinor changes in presentation, results unchanged

References in corpus (22)

• New Symmetries of Massless QED
• Evidence for a New Soft Graviton Theorem
• Low's Subleading Soft Theorem as a Symmetry of QED
• Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance
• On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons
• Loop Corrections to Soft Theorems in Gauge Theories and Gravity
• Factorization Properties of Soft Graviton Amplitudes
• An electromagnetic analog of gravitational wave memory
• Classical and Quantum Results on Logarithmic Terms in the Soft Theorem in Four Dimensions
• Subleading soft photons and large gauge transformations
• Soft Photon and Graviton Theorems in Effective Field Theory
• Asymptotic Symmetries and Electromagnetic Memory
• Infinite Set of Soft Theorems in Gauge-Gravity Theories as Ward-Takahashi Identities
• Asymptotic $U(1)$ charges at spatial infinity
• Observational Signature of the Logarithmic Terms in the Soft Graviton Theorem
• Classical Sub-subleading Soft Photon and Soft Graviton Theorems in Four Spacetime Dimensions
• Electromagnetic Memory
• Infinite Soft Theorems from Gauge Symmetry
• Loop Corrected Soft Photon Theorem as a Ward Identity
• A Classical Proof of the Classical Soft Graviton Theorem in D>4
• Asymptotic charges in massless QED revisited: A view from Spatial Infinity
• New Asymptotic Conservation laws for Electromagnetism

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