Quantum Theory of Electrodynamics in Linear Media Subject to Boundary Conditions
We show that the material dependencies of macroscopically quantized fields in linear media are not consistent with the classical electromagnetic boundary conditions. We then phenomenologically construct macroscopic quantized fields that satisfy quantum--classical correspondence with the result indicating that the canonical momentum in a linear medium is modified as a consequence of the reduced speed of light. We re-derive D'Alembert's principle and Lagrange's equations for an arbitrarily large region of space in which light signals travel slower than in the vacuum and show that the resulting modifications to Lagrangian dynamics, including the canonical momenta, repair the violation of the correspondence principle for macroscopically quantized fields.