In weakly inhomogeneous media, Maxwell equations assume a Dirac-like form that is particularly apt for the study of paraxial propagation. Using this form, and via the Foldy-Wouthuysen transformation technique of the Dirac equation, we study the spin transport of paraxial light beams in weakly inhomogeneous media. We derive the Berry effect terms and establish the spin Hall effect and the Rytov rotation law for polarized paraxial beam transport.PACS numbers: 03.65. Vf,42.25.Bs,

In the framework of the single-field slow-roll inflation, we derive the Hamiltonian of the linear primordial scalar and tensor perturbations in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes in terms of the Lewis-Riesenfeld phase. We conclude by discussing the discrepancy in the results of Pal et. al [Class. Quant. Grav. 30, 12 (2013)] for these Berry phases, which is resolved to yield agreement with our results.

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By using the conformal equivalence of f(R) gravity in vacuum and the usual Einstein theory with scalar-field matter, we derive the Hamiltonian of the linear cosmological scalar and tensor perturbations in f(R) gravity in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes as a Lewis–Riesenfeld phase.