The asymptotic structure of electromagnetism in higher spacetime dimensions

Abstract

We investigate the asymptotic structure of electromagnetism in Minkowski space in even and odd spacetime dimensions $\ge 4$. We focus on $d>4$ since the case $d=4$ has been studied previously at length. We first consider spatial infinity where we provide explicit boundary conditions that admit the known physical solutions and make the formalism well defined (finite symplectic structure and charges). Contrary to the situation found in $d=4$ dimensions, there is no need to impose parity conditions under the antipodal map on the leading order of the fields when $d>4$. There is, however, the same need to modify the standard bulk symplectic form by a boundary term at infinity involving a surface degree of freedom. This step makes the Lorentz boosts act canonically. Because of the absence of parity conditions, the theory is found to be invariant under two independent algebras of angle-dependent $u(1)$ transformations ($d>4$). We then integrate the equations of motion in order to find the behaviour of the fields near null infinity. We exhibit the radiative and Coulomb branches, characterized by different decays and parities. The analysis yields generalized matching conditions between the past of ${\mathcal{I}}^{+}$ and the future of ${\mathcal{I}}^{-}$.

arXiv comment46 pages

References in corpus (40)

• The Dynamics of General Relativity
• On BMS Invariance of Gravitational Scattering
• Aspects of the BMS/CFT correspondence
• BMS supertranslations and Weinberg's soft graviton theorem
• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• New Symmetries of Massless QED
• Asymptotic Symmetries of Yang-Mills Theory
• New Gravitational Memories
• Evidence for a New Soft Graviton Theorem
• Bondi-Sachs Formalism
• Higher-Dimensional Supertranslations and Weinberg's Soft Graviton Theorem
• Asymptotic Flatness and Bondi Energy in Higher Dimensional Gravity
• Magnetic Corrections to the Soft Photon Theorem
• BMS Supertranslations and Memory in Four and Higher Dimensions
• BMS Group at Spatial Infinity: the Hamiltonian (ADM) approach
• BMS Supertranslations and Not So Soft Gravitons
• Null infinity, the BMS group and infrared issues
• A Critique of Pure String Theory: Heterodox Opinions of Diverse Dimensions
• Einstein-Yang-Mills theory : I. Asymptotic symmetries
• Asymptotic $U(1)$ charges at spatial infinity
• The BMS4 algebra at spatial infinity
• Asymptotic symmetries of electromagnetism at spatial infinity
• Asymptotic symmetries of gravity and soft theorems for massive particles
• The Asymptotic Behavior of Massless Fields and the Memory Effect
• Bondi-type systems near space-like infinity and the calculation of the NP-constants
• Hamiltonian structure and asymptotic symmetries of the Einstein-Maxwell system at spatial infinity
• Asymptotic flatness at null infinity in arbitrary dimensions
• Conformal Null Infinity Does Not Exist for Radiating Solutions in Odd Spacetime Dimensions
• Relaxing the Parity Conditions of Asymptotically Flat Gravity
• Gravitational Memory in Higher Dimensions
• Asymptotic charges from soft scalars in even dimensions
• Peeling or not peeling -- is that the question ?
• On the structure and applications of the Bondi-Metzner-Sachs group
• Note on soft theorems and memories in even dimensions
• Asymptotic Symmetries in $p$-Form Theories
• The Memory Effect for Particle Scattering in Even Spacetime Dimensions
• Noether superpotentials in supergravities
• Bondi-type systems near space-like and null infinity
• Angular momentum at null infinity in higher dimensions
• Asymptotic Symmetries of Maxwell Theory in Arbitrary Dimensions at Spatial Infinity

Cited by in corpus (23)

• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• On asymptotic symmetries in higher dimensions for any spin
• Celestial Holography: Lectures on Asymptotic Symmetries
• The Bondi-Metzner-Sachs group in five spacetime dimensions
• On electromagnetic and colour memory in even dimensions
• Asymptotic realization of the super-BMS algebra at spatial infinity
• Symmetries of the gravitational scattering in the absence of peeling
• Asymptotic structure of the gravitational field in five spacetime dimensions: Hamiltonian analysis
• The 4d/2d correspondence in twistor space and holomorphic Wilson lines
• A note on the asymptotic symmetries of electromagnetism
• Asymptotic symmetries of Yang-Mills fields in Hamiltonian formulation
• Asymptotic structure of the Rarita-Schwinger theory in four spacetime dimensions at spatial infinity
• Synchrotron radiation in odd dimensions
• New Magnetic Symmetries in $(d+2)$-Dimensional QED
• Source and Response Soft Charges for Maxwell Theory on $Ad{S}_d$
• Asymptotic $\mathcal{O}(r)$ gauge symmetries and gauge-invariant Poincaré generators in higher spacetime dimensions
• The asymptotic structure of gravity at spatial infinity in four spacetime dimensions
• $\mathcal{O}(r^N)$ two-form asymptotic symmetries and renormalized charges
• Conserved asymptotic charges for any massless particle
• Asymptotic symmetries of scalar electrodynamics and of the abelian Higgs model in Hamiltonian formulation
• Super-Hawking Radiation
• Topics in Asymptotic Symmetries and Infrared Effects
• On well-posedness and algebraic type of the five-dimensional charged rotating black hole with two equal-magnitude angular momenta