Maxwell-Proca theory: Definition and construction

Díez, Verónica Errasti; Gording, Brage; Méndez-Zavaleta, Julio A.; Schmidt-May, Angnis

doi:10.1103/physrevd.101.045009

Cited by 24 publications

(16 citation statements)

References 100 publications

(131 reference statements)

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“…Besides and as we shall explain in Sec. V B, our forthcoming elementary calculations turn out to be enough to understand the complete set of manifestly first-order (self-) interactions among an arbitrary number of both Maxwell and (generalized) Proca [30] fields in four-dimensional flat spacetime [8,9]. This hints to the convenience of the proposed method, compared to other possible approaches, a point that shall be reinforced in the more elaborate examples of the next Sec.…”

Section: Simple Examples: Vector Field Theoriesmentioning

confidence: 70%

“…On shell, we obtain l: the total number of functionally independent Lagrangian constraints. Our analysis elaborates on the iterative algorithm presented in [1] and employed in Appendix A of [8]. It is the suitable generalization to field theory of the coordinate-dependent method used in [2] for particle systems, which is in turn based on [20].…”

Section: Exposition Of the Methodsmentioning

confidence: 99%

“…IV. Their study is cornerstone to understand the Maxwell-Proca theory [8,9] and paves the way to its consistent coupling to gravity. This is discussed in Sec.…”

Section: A Organization Of the Papermentioning

confidence: 99%

“…We point out that, in obtaining this expressions, we have employed the on-shell statement (2.11), so as to eliminate from (2.20) as much dependence on the generalized accelerations̈Q A as possible. 8 Here,W IJ is the so-called secondary Hessian and the auxiliary matrix M AB is the Moore-Penrose pseudoinverse (as detailed in [27]) of the primary Hessian. The latter is ensured to always exist and be unique.…”

Section: Secondary Stagementioning

confidence: 99%

“…A specific materialization of the preceding general discussion (and the one we later on employ to ground our conversion proposal) is as follows. We recall that an earlier version of the method here augmented and refined already allowed for the development of the most general nonlinear multivector field theory over four-dimensional flat spacetime: the Maxwell-Proca theory [8,9]. There, the inclusion of a dynamical gravitational field was beyond scope.…”

Section: Introductionmentioning

confidence: 99%

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Lagrangian constraint analysis of first-order classical field theories with an application to gravity

et al. 2020

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We present a method that is optimized to explicitly obtain all the constraints and thereby count the propagating degrees of freedom in (almost all) manifestly first-order classical field theories. Our proposal uses as its only inputs a Lagrangian density and the identification of the a priori independent field variables it depends on. This coordinate-dependent, purely Lagrangian approach is complementary to and in perfect agreement with the related vast literature. Besides, generally overlooked technical challenges and problems derived from an incomplete analysis are addressed in detail. The theoretical framework is minutely illustrated in the Maxwell, Proca and Palatini theories for all finite d ≥ 2 spacetime dimensions. Our novel analysis of Palatini gravity constitutes a noteworthy set of results on its own. In particular, its computational simplicity is visible, as compared to previous Hamiltonian studies. We argue for the potential value of both the method and the given examples in the context of generalized Proca and their coupling to gravity. The possibilities of the method are not exhausted by this concrete proposal.

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Section: Simple Examples: Vector Field Theoriesmentioning

confidence: 70%

Section: Exposition Of the Methodsmentioning

confidence: 99%

“…IV. Their study is cornerstone to understand the Maxwell-Proca theory [8,9] and paves the way to its consistent coupling to gravity. This is discussed in Sec.…”

Section: A Organization Of the Papermentioning

confidence: 99%

Section: Secondary Stagementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Lagrangian constraint analysis of first-order classical field theories with an application to gravity

et al. 2020

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Proca Metamaterials, Massive Electromagnetism, and Spatial Dispersion

Mikki

2021

Annalen der Physik

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A 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.

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Constant‐Roll Inflation in the Generalized SU(2) Proca Theory

et al. 2022

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The generalized SU(2) Proca theory (GSU2P) is a variant of the well known generalized Proca theory where the vector field belongs to the Lie algebra of the SU(2) group of global transformations under which the action is made invariant. New interesting possibilities arise in this framework because of the existence of new interactions of purely non-Abelian character and new configurations of the vector field resulting in spatial spherical symmetry and the cosmological dynamics being driven by the propagating degrees of freedom. We study the 2D phase space of the system that results when the cosmic triad configuration is employed in the Friedmann-Lemaitre-Robertson-Walker background and find an attractor curve whose attraction basin both covers almost all the allowed region and does not include a Big-Bang singularity. Such an attractor curve corresponds to a primordial inflationary solution that has the following characteristic properties: 1) it is a de Sitter solution whose Hubble parameter is regulated by a generalized version of the SU(2) group coupling constant, 2) it is constant-roll including, as a limiting case, the slow-roll variety, 3) a number of e-folds N > 60 is easily reached, 4) it has a graceful exit into a radiation dominated period powered by the canonical kinetic term of the vector field and the Einstein-Hilbert term. The free parameters of the action are chosen such that the tensor sector of the theory is the same as that of general relativity at least up to second-order perturbations, thereby avoiding the presence of ghost and Laplacian instabilities in the tensor sector as well as making the gravity waves propagate at light speed. This is a proof of concept of the interesting properties that could be found in this scenario when the coupling constants be replaced by general coupling functions and more terms be discovered in the GSU2P.

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Maxwell-Proca theory: Definition and construction

Cited by 24 publications

References 100 publications

Lagrangian constraint analysis of first-order classical field theories with an application to gravity

Lagrangian constraint analysis of first-order classical field theories with an application to gravity

Proca Metamaterials, Massive Electromagnetism, and Spatial Dispersion

Constant‐Roll Inflation in the Generalized SU(2) Proca Theory

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