A nonminimal coupling η has been attracting growing interest particularly in the context of inflation models, though its quantum nature is not clear yet. We study the renormalization of η in the ...scalar quantum electrodynamics (QED). There are one-loop diagrams, which could give the finite correction to η in the scalar QED. We find that they cancel with each other. We also find no inhomogeneous term of the renormalization group equation (RGE) at the two-loop level, while there could be the two-loop order finite correction. This is similar to other theories, where an inhomogeneous term of the RGE appears only at a higher-loop order: e.g., four-loop order in λϕ4 theory.
Abstract
This work shows incompleteness and inconsistency in classical electrodynamics (CED) and quantum electrodynamics (QED). Extended electrodynamics (EED) resolves these issues. ...Stueckelberg-Horwitz-Piron (SHP) theory is equivalent to EED with important implications.
Strong light-matter coupling provides a promising path for the control of quantum matter where the latter is routinely described from first principles. However, combining the quantized nature of ...light with this ab initio tool set is challenging and merely developing as the coupled light-matter Hilbert space is conceptually different and computational cost quickly becomes overwhelming. In this work, we provide a nonperturbative photon-free formulation of quantum electrodynamics (QED) in the long-wavelength limit, which is formulated solely on the matter Hilbert space and can serve as an accurate starting point for such ab initio methods. The present formulation is an extension of quantum mechanics that recovers the exact results of QED for the zero- and infinite-coupling limit and the infinite-frequency as well as the homogeneous limit, and we can constructively increase its accuracy. We show how this formulation can be used to devise approximations for quantum-electrodynamical density-functional theory (QEDFT), which in turn also allows us to extend the ansatz to the full minimal-coupling problem and to nonadiabatic situations. Finally, we provide a simple local density-type functional that takes the strong coupling to the transverse photon degrees of freedom into account and includes the correct frequency and polarization dependence. This QEDFT functional accounts for the quantized nature of light while remaining computationally simple enough to allow its application to a large range of systems. All approximations allow the seamless application to periodic systems.
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