Virtual Photon Model by Spatio-Temporal Vortex Dynamics

Abstract

The issue on theoretical foundation of optical near field or dressed photon (DP) as its quantum mechanical representation in the field of nanophotonics remains unsettled. Experimental data accumulated so far seem to suggest that DP possesses characteristics of off-shell virtual photons. On the basis of this observation and critical reviews of classical as well as quantum theory of light, we are now developing a novel theory describing DP. A unique feature of the theory explained here is that it takes an important role played by spacelike momentum to describe field interactions into consideration and hence it provides an extended picture of conventional virtual photon dynamics on spacetime. We show here that the new model is closely related to so-called “scalar photon” and longitudinal mode of free electromagnetic waves that are eliminated as unphysical modes in a covariant quantization of electromagnetic wave field. So, as an important preliminary step toward constructing a new model of virtual photons, we first discuss that the above prevailing claim made by a covariant quantization theory only reflects dynamical requirement on the micro quantum world and overlooks the emergence of condensed classical modes which can be understood in the framework of Ojima’s Micro-Macro Duality Scheme (MMDS) providing a mathematically derived quantum-classical correspondence. As a matter of fact, the existence of those eliminated “unphysical” modes are clearly reported in the field of classical electromagnetic theory in addition to the fact that those modes are directly related to Coulomb modes playing a significant role in electromagnetic interactions. As a central theme of this article, a newly introduced Clebsch dual field of electromagnetic wave field as an extension of conventional electromagnetic one is shown to be a promising new model of DP as virtual photons. We also point out an intriguing property that extended virtual photons with spacelike property carry negative scalar curvature similar to enigmatic dark energy discussed in cosmology.