Massive Electromagnetism Research Articles

Implications of nonzero photon mass on plasma equilibria.

The Beltrami state in a single-species (electron or ion) ideal plasma in the context of massive electromagnetism has been explored. The inclusion of photon mass, essentially treating the massive photon field as a mobile fluid in the ideal plasma vortical dynamics, has resulted in a triple curl Beltrami state of the magnetic vector potential A[over ⃗]. A variational principle is constructed which shows this state can also be obtained by constrained minimization of the system's energy with appropriate helicity invariants. Such a state is endowed with three different length scales; one of which is the system length, and the other two are species' skin depth and photon Compton wavelength, respectively. An analytical solution of this state in the cylindrical geometry is presented, which is the linear combination of three single Beltrami states. Possible observational signatures of this state in astrophysical and laboratory settings are also discussed.

Cohering and decohering power of massive scalar fields under instantaneous interactions

Employing a non-perturbative approach based on an instantaneous interaction between a two-level Unruh-DeWitt detector and a massive scalar field, we investigate the ability of the field to generate or destroy coherence in the detector by deriving the cohering and decohering power of the induced quantum evolution channel. For a field in a coherent state a previously unnoticed effect is reported whereby the amount of coherence that the field generates displays a revival pattern with respect to the size of the detector. It is demonstrated that by including mass in a thermal field the set of maximally coherent states of the detector decoheres less compared to a zero mass. In both of the examples mentioned, by making a suitable choice of detector radius, field energy and coupling strength it is possible to infer the mass of the field by either measuring the coherence present in the detector in the case of an interaction with a coherent field or the corresponding decoherence of a maximally coherent state in the case of a thermal field. In view of recent advances in the study of Proca metamaterials, these results suggest the possibility of utilising the theory of massive electromagnetism for the construction of novel applications for use in quantum technologies.

Directive properties of radiating source systems in massive electromagnetism

We investigate the problem of electromagnetic radiation in massive electromagnetism with focus on the directive radiation characteristics of Proca antennas (sources embedded into Proca metamaterial domains.) It is theoretically demonstrated that the recently proposed nonlocal Proca metamaterial implies the existence of point nonlocal sources possessing a perfectly isotropic radiation pattern. Based on rigorous analysis, we derive exact expressions for the directive radiation patterns of arbitrary discrete distributions of Proca source systems, i.e., radiating arrays emitting massive photons. Examples of linear discrete Proca arrays are given and comparison with massless photon radiation sources is provided.

Proca Metamaterials, Massive Electromagnetism, and Spatial Dispersion

AbstractA class of electromagnetic metamaterials (MTMs) is investigated, which the author dubs Proca MTMs, constituting a medium behaving like a “relativistic material” for potential use in electromagnetic applications. This work is motivated by numerous previous results on particular structures such as plasma, waveguides, photonic crystals, magnetic materials, where it has been observed that photons may acquire mass in some dispersive domains. In this approach, it is rigorously proved using a field‐theoretic approach that Maxwell theory inside certain classes of nonlocal (spatially‐dispersive) metamaterials is equivalent to Proca theory in vacuum, where in the latter photons acquire a nonzero mass (massive electromagnetism.) An explicit closed‐form general expression for the Proca MTM dielectric function is given. It turns out that the key to the operation of Proca MTM is spatial dispersion, and hence Proca MTMs represent an important example of the more general family of nonlocal MTMs. The author's analysis involves multiphysics aspects, utilizing concepts and methods taken from classical electromagnetism, special relativity, quantum theory, electromagnetic materials, and antenna theory. Extensive discussion of the physics, computational methods, and design parameters of Proca MTMs is provided to further understand the nature of massive electromagnetism in nonlocal (spatially‐dispersive) MTMs. As a concrete application, the main ingredients of Proca antennas are developed as an example of the emerging technology of nonlocal antennas, where the author establishes that a single Proca dipole possesses a perfect isotropic radiation pattern, a noteworthy departure from conventional local antennas (radiators in vacuum and temporally dispersive media) where such radiation characteristics is impossible.

Axiomatic derivation of coincident general relativity and its premetric extension

A theory of gravity is deduced from the axioms of the premetric program. The starting point is the conservation of energy and momenta, and the equivalence of gravitation and inertia. The latter is what leads to the framework of the so-called purified gravity. The local and linear constitutive relation has 14 components when it is assumed to be metrical, but the compatibility of the constitutive relation with an action principle fixes uniquely the theory of coincident general relativity. The premetric formalism of purified gravity has a direct analogy with massive electromagnetism, the Planck mass corresponding to the Proca mass of the gauge boson. The metric emerges as a Stueckelberg field, and the graviton as a Goldstone boson of the broken symmetry.

What Are Observables in Hamiltonian Einstein–Maxwell Theory?

Is change missing in Hamiltonian Einstein-Maxwell theory? Given the most common definition of observables (having weakly vanishing Poisson bracket with each first-class constraint), observables are constants of the motion and nonlocal. Unfortunately this definition also implies that the observables for massive electromagnetism with gauge freedom (Stueckelberg) are inequivalent to those of massive electromagnetism without gauge freedom (Proca). The alternative Pons-Salisbury-Sundermeyer definition of observables, aiming for Hamiltonian-Lagrangian equivalence, uses the gauge generator G, a tuned sum of first-class constraints, rather than each first-class constraint separately, and implies equivalent observables for equivalent massive electromagnetisms. For General Relativity, G generates 4-dimensional Lie derivatives for solutions. The Lie derivative compares different space-time points with the same coordinate value in different coordinate systems, like 1 a.m. summer time vs. 1 a.m. standard time, so a vanishing Lie derivative implies constancy rather than covariance. Requiring equivalent observables for equivalent formulations of massive gravity confirms that G must generate the 4-dimensional Lie derivative (not 0) for observables. These separate results indicate that observables are invariant under internal gauge symmetries but covariant under external gauge symmetries, but can this bifurcated definition work for mixed theories such as Einstein-Maxwell theory? Pons, Salisbury and Shepley have studied G for Einstein-Yang-Mills. For Einstein-Maxwell, both the electromagnetic field strength F and the metric g are invariant under electromagnetic gauge transformations and covariant (changing by a Lie derivative) under 4-dimensional coordinate transformations. Using the bifurcated definition, these quantities count as observables, as one would expect on non-Hamiltonian grounds.

What Are Observables in Hamiltonian Einstein\u2013Maxwell Theory?

Is change missing in Hamiltonian Einstein–Maxwell theory? Given the most common definition of observables (having weakly vanishing Poisson bracket with each first-class constraint), observables are constants of the motion and nonlocal. Unfortunately this definition also implies that the observables for massive electromagnetism with gauge freedom (‘Stueckelberg’) are inequivalent to those of massive electromagnetism without gauge freedom (‘Proca’). The alternative Pons–Salisbury–Sundermeyer definition of observables, aiming for Hamiltonian–Lagrangian equivalence, uses the gauge generator G, a tuned sum of first-class constraints, rather than each first-class constraint separately, and implies equivalent observables for equivalent massive electromagnetisms. For General Relativity, G generates 4-dimensional Lie derivatives for solutions. The Lie derivative compares different space-time points with the same coordinate value in different coordinate systems, like 1 a.m. summer time versus 1 a.m. standard time, so a vanishing Lie derivative implies constancy rather than covariance. Requiring equivalent observables for equivalent formulations of massive gravity confirms that G must generate the 4-dimensional Lie derivative (not 0) for observables. These separate results indicate that observables are invariant under internal gauge symmetries but covariant under external gauge symmetries, but can this bifurcated definition work for mixed theories such as Einstein–Maxwell theory? Pons, Salisbury and Shepley have studied G for Einstein–Yang–Mills. For Einstein–Maxwell, both F_{mu nu } and g_{mu nu } are invariant under electromagnetic gauge transformations and covariant (changing by a Lie derivative) under 4-dimensional coordinate transformations. Using the bifurcated definition, these quantities count as observables, as one would expect on non-Hamiltonian grounds.

Equivalent Theories and Changing Hamiltonian Observables in General Relativity

Change and local spatial variation are missing in Hamiltonian general relativity according to the most common definition of observables as having 0 Poisson bracket with all first-class constraints. But other definitions of observables have been proposed. In pursuit of Hamiltonian–Lagrangian equivalence, Pons, Salisbury and Sundermeyer use the Anderson–Bergmann–Castellani gauge generator G, a tuned sum of first-class constraints. Kuchař waived the 0 Poisson bracket condition for the Hamiltonian constraint to achieve changing observables. A systematic combination of the two reforms might use the gauge generator but permit non-zero Lie derivative Poisson brackets for the external gauge symmetry of General Relativity. Fortunately one can test definitions of observables by calculation using two formulations of a theory, one without gauge freedom and one with gauge freedom. The formulations, being empirically equivalent, must have equivalent observables. For de Broglie-Proca non-gauge massive electromagnetism, all constraints are second-class, so everything is observable. Demanding equivalent observables from gauge Stueckelberg–Utiyama electromagnetism, one finds that the usual definition fails while the Pons–Salisbury–Sundermeyer definition with G succeeds. This definition does not readily yield change in GR, however. Should GR’s external gauge freedom of general relativity share with internal gauge symmetries the 0 Poisson bracket (invariance), or is covariance (a transformation rule) sufficient? A graviton mass breaks the gauge symmetry (general covariance), but it can be restored by parametrization with clock fields. By requiring equivalent observables, one can test whether observables should have 0 or the Lie derivative as the Poisson bracket with the gauge generator G. The latter definition is vindicated by calculation. While this conclusion has been reported previously, here the calculation is given in some detail.

Stueckelberg massive electromagnetism in de Sitter and anti–de Sitter spacetimes: Two-point functions and renormalized stress-energy tensors

By considering Hadamard vacuum states, we first construct the two-point functions associated with Stueckelberg massive electromagnetism in de Sitter and anti--de Sitter spacetimes. Then, from the general formalism developed by Belokogne and Folacci [Phys. Rev. D 93, 044063 (2016)], we obtain an exact analytical expression for the vacuum expectation value of the renormalized stress-energy tensor of the massive vector field propagating in these maximally symmetric spacetimes.

Dispersion by pulsars, magnetars, fast radio bursts and massive electromagnetism at very low radio frequencies

Our understanding of the universe relies mostly on electromagnetism. As photons are the messengers, fundamental physics is concerned in testing their properties. Photon mass upper limits have been earlier set through pulsar observations, but new investigations are offered by the excess of dispersion measure (DM), sometimes observed with pulsar and magnetar data at low frequencies, or with the fast radio bursts (FRBs), of yet unknown origin. Arguments for the excess of DM do not reach a consensus, but are not mutually exclusive. Thus, we remind that for massive electromagnetism, dispersion goes as the inverse of the frequency squared. Thereby, new avenues are offered also by the recently operating ground observatories in 10–80MHz domain and by the proposed Orbiting Low Frequency Antennas for Radio astronomy (OLFAR). The latter acts as a large aperture dish by employing a swarm of nano-satellites observing the sky for the first time in the 0.1–15MHz spectrum. The swarm must be deployed sufficiently away from the ionosphere to avoid distorsions from terrestrial interference, especially during solar maxima, and offer stable conditions for calibration during observations.

Stueckelberg massive electromagnetism in curved spacetime: Hadamard renormalization of the stress-energy tensor and the Casimir effect

We discuss Stueckelberg massive electromagnetism on an arbitrary four-dimensional curved spacetime (gauge invariance of the classical theory and covariant quantization, wave equations for the massive spin-1 field $A_\mu$, for the auxiliary Stueckelberg scalar field $\Phi$ and for the ghost fields $C$ and $C^\ast$, Ward identities, Hadamard representation of the various Feynman propagators and covariant Taylor series expansions of the corresponding coefficients). This permits us to construct, for a Hadamard quantum state, the expectation value of the renormalized stress-energy tensor associated with the Stueckelberg theory. We provide two alternative but equivalent expressions for this result. The first one is obtained by removing the contribution of the "Stueckelberg ghost" $\Phi$ and only involves state-dependent and geometrical quantities associated with the massive vector field $A_\mu$. The other one involves contributions coming from both the massive vector field and the auxiliary Stueckelberg scalar field, and it has been constructed in such a way that, in the zero-mass limit, the massive vector field contribution reduces smoothly to the result obtained from Maxwell's theory. As an application of our results, we consider the Casimir effect outside a perfectly conducting medium with a plane boundary. We discuss the results obtained using Stueckelberg but also de Broglie-Proca electromagnetism and we consider the zero-mass limit of the vacuum energy in both theories. We finally compare the de Broglie-Proca and Stueckelberg formalisms and highlight the advantages of the Stueckelberg point of view, even if, in our opinion, the de Broglie-Proca and Stueckelberg approaches of massive electromagnetism are two faces of the same field theory.

Cosmological topologically massive gravitons and photons**Some of these results were reported in abbreviated form in [1

We study topologically massive (2+1)-dimensional gravity with a negative cosmological constant. The masses of the linearized curvature excitations about AdS3 backgrounds are not only shifted from their flat background values but also, more surprisingly, split according to chirality. For all finite values of the topological mass, we find a single bulk degree of freedom with positive energy, and exhibit a complete set of normalizable, finite-energy wave packet solutions. This model can also be written as a sum of two higher-derivative Chern–Simons theories, weighted by the central charges of the boundary conformal field theory. At two particular ‘critical’ values of the couplings, one of these central charges vanishes, and linearized topologically massive gravity becomes equivalent to topologically massive electromagnetism; however, the physics of the bulk wave packets remains unaltered here.

On massive electromagnetism in the null-plane: their limit and ‘‘dual’’ invariance

The limiting process is developed, stressing the simplicity of the null-plane formulation. A SU(2) ‘‘dual’’ invariance for the dynamical variables is made explicit. The symmetry is not satisfied by the field strengths.