Abstract
In an isotropic background comprised of free charges, the transverse and longitudinal modes of the photon acquire large corrections to their dispersion relations, described by the in-medium photon self-energy. Previous work has developed simple approximations that describe the propagation of on-shell photons in plasmas of varying temperatures and densities. However, off-shell excitations can also receive large medium-induced corrections, and the on-shell approximations have often been used in an effort to capture these effects. In this work we show that the off-shell self-energy can be qualitatively very different than the on-shell case. We develop analytic approximations that are accurate everywhere in phase space, especially in classical and degenerate plasmas. From these, we recover the on-shell expressions in the appropriate limit. Our expressions also reproduce the well-known Lindhard response function from solid-state physics for the longitudinal mode.
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Acknowledgments
It is a pleasure to thank Nirmalya Brahma, Simon Caron-Huot, Charles Gale, Saniya Heeba, and Oscar Hernández for useful conversations pertaining to this work and comments on the manuscript. We especially thank Tongyan Lin for pointing out the connection between our work and the Lindhard response function. HS was supported in part by a Master research scholarship from the Fonds de recherche du Québec – Nature et technologies (FRQNT). KS and HS acknowledge support from the Programme Établissement de la relève professorale from the FRQNT, from a Natural Sciences and Engineering Research Council of Canada Subatomic Physics Discovery Grant, and from the Canada Research Chairs program. KS thanks the Kavli Institute for the Physics and Mathematics of the Universe and the Kavli Institute for Theoretical Physics (supported by grant NSF PHY-2309135) for their hospitality in the late stages of the completion of this work. This analysis made use of Numpy [43], Scipy [44], Matplotlib [45], and Mathematica [46].
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Schérer, H., Schutz, K. Photon self-energy at all temperatures and densities in all of phase space. J. High Energ. Phys. 2024, 139 (2024). https://doi.org/10.1007/JHEP11(2024)139
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DOI: https://doi.org/10.1007/JHEP11(2024)139