As an important follow-up report on the latest study of the first author (H.S.) on an off-shell quantum field causing a dressed photon and dark energy, we further discuss a couple of intriguing subjects based on our new theory. One is the dressed photon constant. If we use it, in addition to h¯ and c, as the third component of natural units, then it is defined as the geometric mean of the smallest and the largest lengths: Planck length and that relating to the cosmological constant. Interestingly, this length (≈ 50 nanometers) seems to give a rough measure of the Heisenberg cut for electromagnetic phenomena. The other is a new perspective on cosmology that combines two original notions, i.e., twin universes and conformal cyclic cosmology, proposed respectively by Petit and Penrose, into one novel picture where universes expand self-similarly. We show the possibility that twin universes having a dual structure of [matter with (dark energy & matter)] vs. corresponding anti-entities, separated by an event horizon embedded in the geometric structure of de Sitter space, undergo endless cyclic processes of birth and death, as in the case of the pair creation and annihilation of elementary particles through the intervention of a conformal light field.

In this paper, we investigate the so-called electronic dressed states, a unified quasiparticle resulting from the interaction between electrons in a two-dimensional material with an off-resonance optical dressing field. If the frequency of this field is much larger than all characteristic energies in the system, such as the Fermi energy or bandgap(s), the electronic band structure is affected by radiation so that some important properties of the electron dispersions could be modified in a way desirable for practical applications. For example, a circularly polarized light can be used to vary the bandgap of Dirac materials: it opens a gap in graphene and other metallic and semimetallic lattices, or modifies the magnitude of an existing gap. This will either enhance or reduce a gap, depending on its initial value as well as properties of a host material. Here, we consider gaped dice and Lieb lattices as samples, and put forward a full theoretical model to reveal how these electronic states are deformed by an elliptically-polarized irradiation with a focus on generation and modification of a bandgap.