Abstract
In [1], the authors argued that the Newman-Janis algorithm on the space of classical solutions in general relativity and electromagnetism could be used in the space of scattering amplitudes to map an amplitude with external scalar states to an amplitude associated to the scattering of “infinite spin particles”. The minimal coupling of these particles to the gravitational or Maxwell field is equivalent to the classical coupling of the Kerr blackhole with linearized gravity or the so-called \( \sqrt{\textrm{Kerr}} \) charged state with the electromagnetic field. The action of the Newman-Janis mapping on scattering amplitudes was then used to compute the linear impulse at first post-Minkowskian (1PM) order, via the Kosower, Maybee, O’Connell (KMOC) formalism. In this paper, we continue with the idea of using the Newman-Janis mapping on the space of scalar QED amplitudes to compute classical observables such as the radiative gauge field and the angular impulse. We show that for tree-level amplitudes, the Newman-Janis action can be reinterpreted as a dressing of the photon propagator. This turns out to be an efficient way to compute these classical observables. Along the way, we highlight a subtlety that arises in proving the conservation of angular momentum for scalar \( -\sqrt{\textrm{Kerr}} \) scattering.
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Acknowledgments
We are grateful to Alok Laddha for suggesting the problem and numerous insightful discussions. We thank him for carefully going through the draft and providing valuable suggestions and comments on it. We thank Sujay Ashok for constant encouragement and valuable comments on the draft. We thank all the participants of ‘Amplitudes @ Chennai’ workshop at the Chennai Mathematical Institute for interesting discussions. SA would like to thank the organizers of the ‘Indian Strings Meeting 2023’ at the Indian Institute of Technology Bombay for an opportunity to present a part of this work as a poster, and the participants for their feedback. We also thank Yilber Fabian Bautista and Rafael A. Porto for their feedback and discussion. AM thanks Aninda Sinha for support and acknowledges financial support from DST through the SERB core grant CRG/2021/000873.
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Akhtar, S., Manna, A. & Manu, A. Classical observables using exponentiated spin factors: electromagnetic scattering. J. High Energ. Phys. 2024, 148 (2024). https://doi.org/10.1007/JHEP05(2024)148
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DOI: https://doi.org/10.1007/JHEP05(2024)148