Massive Electrodynamics Research Articles

A connection between massive electrodynamics and the Einstein-Maxwell equations

Quaternions are the best mathematical construct for creatingvarious equations in electrodynamics, which has led to the emergence of new terms with unique physical implications. Since quaternions also have noncommutative properties that are reflected in curved space-time too, a formulation of a theory using quaternions can be compared with that formulated in some curved space-time. Furthermore, we calculate the Maxwell equations in curved space-time and observe the presence of extra terms that are not present in flat space-time. An electric current arises because of the coupling between the magnetic field and curvature. Upon comparing the outcomes of the two methods, we discovered a correlation between mass and gravity, indicating their similarity. Equations formulated via quaternions are equivalent to those formulated in curved space-time. The optical chirality and its flux are generalized to massive electrodynamics.

Duality as a method to derive a gauge invariant massive electrodynamics and new interactions

Duality as a method to derive a gauge invariant massive electrodynamics and new interactions

The 3-dimensional and 2-dimensional Cerenkov effect with massive photons

The equations of massive electrodynamics are derived and the power spectrum formula for the 3-dimensional Cerenkov radiation of massive photons is found. It is argued that the massive Cerenkov effect can be observed in superconductive media, ionosphere plasma, waveguides and in particle laboratories. The same is valid for the Cerenkov radiation in the 2-dimensional medium including silicene. The 2D-Cerenkov effect with the massless photons was observed by the famous world laboratories (Adiv et al., 2022).

The dual continuity equations

The ordinary continuity equation relating to the current and density of a system is extended to incorporate systems with dual (longitudinal and transverse) currents. Such a system of equations is found to have the same mathematical structure as that of Maxwell equations. The longitudinal and transverse currents and the densities associated with them are found to be coupled with each other. Each of these quantities is found to obey a wave equation traveling at the velocity of light in a vacuum. London equations of super-conductivity are shown to emerge from some sort of continuity equations. The new London equations are symmetric and are shown to be dual to each other. It is shown that London’s equations are Maxwell’s equations with a massive electromagnetic field (photon). These equations preserve the gauge invariance that is broken in other massive electrodynamics. The duality invariance may allow magnetic monopoles to be present inside superconductors. The new duality is called the comprehensive duality transformation.

Induced curvature effects in Maxwell’s equations

We have studied in this work extended electrodynamics with a relaxed Lorenz gauge condition. We then compare it with the electrodynamics in curved space–time. Interestingly, the interaction of the electromagnetic field with the space curvature induces electric and magnetic charges and currents. The coupling of the electromagnetic field with the particle charge gives rise to its spin. Two spins are found to emerge in addition to their associated helicities. The electromagnetic field is found to be coupled to curvature through its electric and magnetic spins. The electrodynamics in curved space is found to be analogous to massive electrodynamics. When the electromagnetic field travels in curved space–time, it acquires mass depending on the strength of the space curvature. In curved space, the space in which the electromagnetic field travels got an effective electric conductivity proportional to the temporal variation of the metric determinant. The curved space appears to behave like a conducting medium with variable electric conductivity. Moreover, an additional current perpendicular to the magnetic field is induced whenever the space is curved. Axion and Chern–Simons electrodynamics are found to be connected to massive electrodynamics and standard electrodynamics in curved space–time.

Comment on “Massive electrodynamics and the magnetic monopoles”

In this paper we correct previous work on magnetic charge plus a photon mass. We show that contrary to previous claims this system has a very simple, closed form solution which is the Dirac string potential multiplied by a exponential decaying part. Interesting features of this solution are discussed, namely, (i) the Dirac string becomes a real feature of the solution, (ii) the breaking of gauge symmetry via the photon mass leads to a breaking of the rotational symmetry of the monopole's magnetic field, (iii) the Dirac quantization condition is potentially altered.

Conformal electrodynamics in curved space

We consider the conformal transformation of electrodynamics in curved space. The invariance of the Lorenz gauge condition under the conformal transformation yields the massive Lorenz gauge condition. The conformal massless electrodynamics in curved space yields massive electrodynamics in Minkowski space. The conformal Klein–Gordon equation in the conformal frame is found to yield the quantum Telegraph equation. The conformal transformation of a given field yields the matter (particle) of the field confirming that the field, like a particle, has a dual nature. A special type of conformal transformation is shown to give massless fields a mass that is tantamount to Higgs mechanics. The parameter (weight) ξ=±1 in the conformal transformation of the electromagnetic tensor, F˜μν=Ω±1Fμν, defines the photon mass in the Minkowski frame.

Maxwell’s electrodynamics including spin and chirality

Maxwell electrodynamics and its modification are derived using quaternionic formulation. Starting from the quaternionic Maxwell’s equation, all subsequent equations are derived in a very succinct way. The energy, momentum, and spin angular momentum conservation equations are defined for quaternionic electrodynamics. Using the modified electrodynamics, we formally derive London’s equations of superconductivity without recourse to Newton’s second law of motion. The modified electrodynamics allows a longitudinal scalar field to arise besides the transverse electromagnetic field. The influence of the scalar field is manifested in several phenomena we already encountered but we have incorporated such effects in the framework of Maxwell’s electrodynamics. The non-uniformity and inhomogeneity of the medium, in which the electromagnetic field exists, affects the electromagnetic properties of the system in the way how the scalar field vary in space and time. Two different scenarios for quantum massive electrodynamics are proposed. One of the scenarios reduces to axion electrodynamics which further reduces to Maxwell–Proca massive boson electrodynamics. A quantum massive electrodynamic is studied and found not to alter the beauty of Maxwell’s electrodynamics. Additional electric and magnetic charge densities are found to be induced with non-dissipative currents.

On the creation of charged massless fermion pair by a photon in an external constant uniform magnetic field in 2+1 dimensions

Creation of charged massless fermion pair by a photon in a constant uniform magnetic field is considered in the one-loop approximation of the [Formula: see text]-dimensional quantum electrodynamics (QED[Formula: see text]). We calculate the elastic scattering amplitude (EAS) of photon using the polarization operator of photon in the above magnetic field obtained earlier in our work. We analyze the elastic scattering amplitude of photon at various values of the photon energy and magnetic field strength. Very simple analytical formulas for EAS of photon are obtained in the so-called quasi-classical region. In the massive quantum electrodynamics the elastic scattering amplitude of photon defines its “mass” squared in the presence of external electromagnetic field and the imaginary part of EAS describes the total probability of charged massive fermion pair creation in the electromagnetic field; we assume that it is the case and in the massless quantum electrodynamics.

Massive photons and electrically charged black holes

The characteristic time of disappearance of electric field in massive electrodynamics during the capture of electric charge by black holes is calculated. It is shown that this time does not depend upon the photon mass. The electric field at large distances disappears with the speed of light.

Anomalous Magnetic Moment of an Electron in a Static Magnetic Field in the Topologically Massive 2D Electrodynamics

An analytic equation for the anomalous magnetic moment of an electron in a static magnetic field in the topologically massive 2D electrodynamics is obtained in the single-loop approximation. The asymptotic expressions describing the dependence of the anomalous magnetic moment on the dimensionless Chern–Simons parameter and the dynamic field parameter are determined in the limiting case of a relatively weak magnetic field. The applicability conditions for the results of calculations of the anomalous electron magnetic moment based on the evaluation of the vertex function in the 2D electrodynamics with the Chern–Simons term are established.

On dynamic aspects of the Proca field screening by a black hole

Classical black holes are known for almost half a century to nullify exterior classical massive vector field associated with a charge crossing the event horizon. This implies that, from the point of view of an external observer, the Proca field of the charge is screened with the strength gradually increasing as the charge adiabatically approaches the event horizon. In this paper we reject the adiabaticity constraint and calculate analytically the field evolution with respect to a distant observer in the frame of the simplest model of a contracting charged spherical shell concentrically surrounding a Schwarzschild black hole. We show that a time scale of the screening is determined by a mass of the black hole and, moreover, loss of Proca hair during the collapse of charged matter has the same temporal character. Due to existence of the event horizon, there is discontinuous jump between massive and massless electrodynamics. This means that presence of an arbitrarily small mass of the photon induces observable effects, which include generation of electric asymmetry of the Universe and galactic magnetic fields.

Dynamic nature of the anomalous magnetic moment of an electron in a constant magnetic field in topologically massive two-dimensional electrodynamics

An analytical expression is obtained for the anomalous magnetic moment of an electron in a constant magnetic field in topologically massive two-dimensional electrodynamics. In the limiting case of a relatively weak magnetic field, asymptotic formulas are found, which specify the dependence of the anomalous magnetic moment on the Chern-Simons parameter and dynamic parameter of synchrotron radiation. The conditions are identified for the applicability of the computations of the anomalous magnetic moment of an electron, which have previously been made based on the calculation of the vertex function in two-dimensional electrodynamics with the Chern-Simons term.

Hamiltonian formalism of topologically massive electrodynamics

We consider the four-dimensional topologically massive electrodynamics in which a gauge field interacts with rank two antisymmetric tensor field through a topological interaction. The photon becomes massive by eating the rank two tensor field, which is dual to the Higgs mechanism. We explicitly demonstrate the nature of the mechanism by performing a canonical analysis of the theory and discuss various aspects of it.

Inflationary magnetic fields from massive Euler–Heisenberg electrodynamics

We study the generation of cosmic magnetic fields during de Sitter inflation in a non-conformally-invariant effective model of massive electrodynamics containing a four-photon interaction term. We show that, if the photon self-coupling is strong enough, comoving magnetic fields correlated on scales of 10kpc and of intensities 10−22G≲B0≲10−19G are produced as excitation of the vacuum. If amplified by galactic dynamo, they naturally explain the existence of galactic magnetic fields.

Large scale magnetic fields from torsion modes and massive photon inflation

Previously, Barrow and Tsagas (2008 Phys. Rev. D 77 107302) showed that a slower decay of magnetic fields are present in open Friedmann universes, with traditional Maxwell equations. In their paper magnetic fields of the order of , which are far below the value required to seed galactic dynamos, were obtained. In this paper, galactic dynamo seeds of the order of are obtained from massive electrodynamics in an Einstein–Cartan–Proca expanding universe of de Sitter type. Slow decay of magnetic fields in photon–torsion coupling in quantum electrodynamics (Garcia de Andrade 2011 Phys. Lett. B 468 28) have been recently shown by the author Garcia de Andrade (2012 Phys. Lett. B 711 143) to also not be able to seed galactic dynamos. Torsion modes are constrained by the field equations. Spacetime torsion is shown to be explicitly responsible for the slow decay of a cosmic magnetic field. In the absence of massive photon torsion coupling the magnetic field decay is of the order , when torsion turns on . The pure massive-photon–torsion contribution amplifies the magnetic field by which characterizes an extremely slow magnetic dynamo action due to purely torsion gravitational effects. Recently Barrow, Tsagas and Yamamoto (2012 Phys. Rev. D 86 023535) have obtained superadiabatic amplification of B-fields in Friedmann open cosmology which lies within and which falls very comfortably within the limits to seed galactic dynamos. The are other simple solutions where a B-field decays as , a relatively weak photon–torsion coupling approximation. These solutions are obtained for de Sitter and Friedmann metrics. Numerical values as displayed in this new version of the paper specifically for GUT phases of inflation with and without massive photons; without photons we obtain the well known value of GR which is while for the values with massive photons one obtains . At the present time one obtains and with massive photons one obtains , which is unfortunately much stronger than the value obtained by astronomical observations of .

Scale magnetic effect in quantum electrodynamics and the Wigner-Weyl formalism

The Scale Magnetic Effect (SME) is the generation of electric current due to conformal anomaly in external magnetic field in curved spacetime. The effect appears in a vacuum with electrically charged massless particles. Similarly to the Hall effect, the direction of the induced anomalous current is perpendicular to the direction of the external magnetic field $\bf B$ and to the gradient of the conformal factor $\tau$, while the strength of the current is proportional to the beta function of the theory. In massive electrodynamics the SME remains valid, but the value of the induced current differs from the current generated in the system of massless fermions. In the present paper we use the Wigner--Weyl formalism to demonstrate that in accordance with the decoupling property of heavy fermions the corresponding anomalous conductivity vanishes in the large-mass limit with $m^2 \gg |e {\bf B}|$ and $m \gg |\nabla \tau|$.

Anomalous magnetic moment of an electron in a magnetized plasma of topologically massive two-dimensional electrodynamics

Anomalous magnetic moment of an electron in a magnetized plasma of topologically massive two-dimensional electrodynamics

Massive photon and dark energy

We investigate cosmology of massive electrodynamics and explore the possibility whether massive photon could provide an explanation of the dark energy. The action is given by the scalar-vector-tensor theory of gravity which is obtained by non-minimal coupling of the massive Stueckelberg QED with gravity and its cosmological consequences are studied by paying a particular attention to the role of photon mass. We find that the theory allows cosmological evolution where the radiation- and matter-dominated epochs are followed by a long period of virtually constant dark energy that closely mimics $\Lambda$CDM model and the main source of the current acceleration is provided by the nonvanishing photon mass governed by the relation $\Lambda\sim m^2$. A detailed numerical analysis shows that the nonvanishing photon mass of the order of $\sim 10^{-34}$ eV is consistent with the current observations. This magnitude is far less than the most stringent limit on the photon mass available so far, which is of the order of $m \leq 10^{-27}$eV.

Higher derivative Chern-Simons extension in the noncommutativeQED3

The noncommutative (NC) massive quantum electrodynamics in $2+1$ dimensions is considered. We show explicitly that the one-loop effective action arising from integrating out the fermionic fields leads to the ordinary NC Chern-Simons and NC Maxwell action at the long wavelength limit (large fermion mass). In the next to leading order, the higher-derivative contributions to NC Chern-Simons are obtained. Moreover, the gauge invariance of the outcome action is carefully discussed. We then consider the higher-derivative modification into the pure NC Chern-Simons Lagrangian density and evaluate the one-loop correction to the pole of the photon propagator.