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Abstract
The relativistic theory of the time and positiondependent energy and momentum densities of light in glasses and other lowloss dispersive media, where different wavelengths of light propagate at different phase velocities, has remained a largely unsolved challenge until now. This is astonishing in view of the excellent overall theoretical understanding of Maxwell's equations and the abundant experimental measurements of optical phenomena in dispersive media. The challenge is related to the complexity of the interference patterns of partial waves and to the coupling of the field and medium dynamics by the optical force on the medium atoms. In this work, we use the masspolariton theory of light [Phys. Rev. A 96, 063834 (2017)] to derive the stressenergymomentum (SEM) tensors of the field and the dispersive medium. Our starting point, the fundamental local conservation laws of energy and momentum densities in classical field theory, is close to that of a recent theoretical work on light in dispersive media by Philbin [Phys. Rev. A 83, 013823 (2011)], which, however, excludes the powerconversion and force density source terms describing the coupling between the field and the medium. In the general inertial frame, we present the SEM tensors in terms of Lorentz scalars, fourvectors, and field tensors that reflect in a transparent way the Lorentz covariance of the theory. The SEM tensors of the field and the medium are symmetric, forminvariant for all inertial observers, and in full accordance with the covariance principle of the special theory of relativity. When the powerconversion and force density source terms are accounted for, there is no need to introduce asymmetric SEM tensors or heuristic symmetrization procedures even for the field and medium subsystems. Therefore, asymmetric SEM tensors based on strictly classical energy and momentum densities, which have been studied in previous literature, do not account for all aspects in the fieldmedium coupling of electromagnetic waves. However, being based on classical field theory, the present work prompts for further groundwork on the classical limit of the quantum mechanical spin of light in a medium. The SEM tensor of the coupled fieldmedium state of light also has zero fourdivergence. Therefore, light in a dispersive medium has a welldefined fourmomentum and rest frame. The volume integrals of the total energy and momentum densities of light agree with the model of masspolariton quasiparticles having a nonzero rest mass. The coupled fieldmedium state of light drives forward an atomic mass density wave, which makes the constant centerofenergy velocity law of an isolated system  a fundamental conservation law of nature  satisfied. This provides strong evidence for the consistency of the theory. The predictions of our work, such as the atomic mass density wave associated with light, are accessible to experiments.
Original language  English 

Article number  023510 
Number of pages  26 
Journal  Physical Review A 
Volume  104 
Issue number  2 
DOIs  
Publication status  Published  13 Aug 2021 
MoE publication type  A1 Journal articlerefereed 
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Dive into the research topics of 'Covariant theory of light in a dispersive medium'. Together they form a unique fingerprint.Projects
 2 Finished

DynaLight: Lightdriven atomic dynamics in solids and liquids – from fundamentals of optics to engineering of novel photonics technologies
01/04/2019 → 31/05/2021
Project: EU: MC

Masspolariton theory of light: from theory to simulation of experiments
Tulkki, J., Partanen, M., Nissilä, I. & Rönn, J.
01/09/2018 → 30/06/2022
Project: Academy of Finland: Other research funding