After imposing the Gauss law constraint as an initial condition upon the Hilbert space of the Nambu model, in all its generic realizations, we recover QED in the corresponding nonlinear gauge A A ¼ n 2 M 2 . Our result is nonperturbative in the parameter M for n 2 Þ 0 and can be extended to the n 2 ¼ 0 case. This shows that, in the Nambu model, spontaneous Lorentz symmetry breaking dynamically generates gauge invariance, provided the Gauss law is imposed as an initial condition. In this way, electrodynamics is recovered, with the photon being realized as the Nambu-Goldstone modes of the spontaneously broken symmetry, which finally turns out to be nonobservable.
We consider two semi-infinite magnetoelecteric media separated by a planar interface whose electromagnetic response is described by axion electrodynamics. The time-dependent Green's function characterizing this geometry is obtained by a method that can be directly generalized to cylindrical and spherical configurations of two magnetoelectrics separated by an interface. We establish the far-field approximation of the Green's function and apply these results to the case of a charged particle moving from one medium to the other at a high constant velocity perpendicular to the interface. From the resulting angular distribution of the radiated energy per unit frequency we provide theoretical evidence for the emergence of reversed Vavilov-Čerenkov radiation in naturally existing magnetoelectric media. In the case where one of the magnetoelectrics is a 3D topological insulator, TlBiSe2, for example, located in front of a regular insulator, we estimate that an average forward Vavilov-Čerenkov radiation with frequency ∼ 2.5 eV (∼ 500 nm) will produce a highly suppressed reversed Vavilov-Čerenkov radiation which can be characterized by an effective frequency in the range of ∼ (4 × 10 −3 − 0.5) meV. However, this value compares favorably with recent measurements in left-handed metamaterials yielding reversed Vavilov-Čerenkov radiation with frequencies of the order of (1.2 − 3.9) × 10 −2 meV. * Electronic address: francamentesantiago@ciencias.unam.mx † Electronic address: urrutia@nucleares.unam.mx ‡ Electronic address: omar.rodriguez@correo.nucleares.unam.mx
We consider two semi-infinite magnetoelectric media with constant dielectric permittivity separated by a planar interface, whose electromagnetic response is described by non-dynamical axion electrodynamics and investigate the radiation of a point-like electric dipole located perpendicularly to the interface. We start from the exact Green's function for the electromagnetic potential, whose far-field approximation is obtained using a modified steepest descent approximation. This procedure yields the standard spherical waves as well as axially symmetric cylindrical superficial waves, which nevertheless are restricted to a region very close to the interface. We compute the angular distribution of the radiation and the total radiated power finding different interference patterns, depending on the relative position dipole-observer, and polarization mixing effects which are all absent in the standard dipole radiation. They are a manifestation of the magnetoelectric effect induced by axion electrodynamics. We illustrate our findings with some numerical estimations employing realistic media as well as some hypothetical choices in order to illuminate the effects of the magnetoelectric coupling which is usually very small.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.