Symmetries, Conserved Properties, Tensor Representations, and Irreducible Forms in Molecular Quantum Electrodynamics

Abstract

In the wide realm of applications of quantum electrodynamics, a non-covariant formulation of theory is particularly well suited to describing the interactions of light with molecular matter. The robust framework upon which this formulation is built, fully accounting for the intrinsically quantum nature of both light and the molecular states, enables powerful symmetry principles to be applied. With their origins in the fundamental transformation properties of the electromagnetic field, the application of these principles can readily resolve issues concerning the validity of mechanisms, as well as facilitate the identification of conditions for widely ranging forms of linear and nonlinear optics. Considerations of temporal, structural, and tensorial symmetry offer significant additional advantages in correctly registering chiral forms of interaction. More generally, the implementation of symmetry principles can considerably simplify analysis by reducing the number of independent quantities necessary to relate to experimental results to a minimum. In this account, a variety of such principles are drawn out with reference to applications, including recent advances. Connections are established with parity, duality, angular momentum, continuity equations, conservation laws, chirality, and spectroscopic selection rules. Particular attention is paid to the optical interactions of molecules as they are commonly studied, in fluids and randomly organised media.

Spin-orbit interactions and chiroptical effects engaging orbital angular momentum of twisted light in chiral and achiral media

“…Conversely, in systematically ordered media, (whether the orientational ordering is total or partial), a lack of full rotational symmetry means that chiroptical effects can be anticipated in either chiral or achiral samples [52][53][54]. As was observed in Section III, E1E2 terms cannot contribute to chiroptical effects in isotropic chiral or achiral media.…”

Chirality in fluorescence and energy transfer

“…It is important to be clear from the outset that the familiar rules for 3D chirality, which demand the absence of any rotation-reflection axesrules that also preclude mirror or inversion symmetryare specifically the requirements for observations of chirality in fluid media. (Two-dimensional and metasurface forms of chirality impose A c c e p t e d M a n u s c r i p t less restrictive, though equally rigorous criteria, and these have been discussed in another recent review) [39].…”

Quantum electrodynamics in modern optics and photonics: tutorial

“…In fact, while externally applied static electric and magnetic fields can be treated as additional zero-frequency perturbations-see, for example, Refs. [30,31]-their effect can also be correctly identified as the result of virtual photon coupling with static multipoles of the corresponding electric or magnetic kind. Adopting this form of coupling enables proper account of the influence of local molecular dipoles and surface potentials, as for example in a recent study of the fluorescence energy transfer at membrane surfaces [32].…”