Proca Field Research Articles

Constraints on metric-Palatini gravity from QPO data

AbstractIn this work, we study metric-Palatini gravity extended by the antisymmetric part of the affine curvature. This gravity theory leads to general relativity plus a geometric Proca field. Using our previous construction of its static spherically-symmetric AdS solution (Eur Phys J. C 83(4):318, 2023), we perform a detailed analysis in this work using the observational quasiperiodic oscillations (QPOs) data. To this end, we use the latest data from stellar-mass black hole GRO J1655-40, intermediate-mass black hole in M82-X1, and the super-massive black hole in SgA* (our Milky Way) and perform a Monte-Carlo-Markov-Chain (MCMC) analysis to determine or bound the model parameters. Our results shed light on the allowed ranges of the Proca mass and other parameters. The results imply that our solutions can cover all three astrophysical black holes. Our analysis can also be extended to more general metric-affine gravity theories.

Chromoelectric flux tubes within non-Abelian Proca theory

Flux tube solutions within non-Abelian SU(3) Proca theory with external sources are obtained. It is shown that such tubes have a longitudinal chromoelectric field possessing two components (nonlinear and gradient), as well as a transverse chromomagnetic field whose force lines create concentric circles with the center on the axis of the tube. The scenario of a possible relationship between non-Abelian Proca theory and quantum chromodynamics is considered. In such scenario: (a) the components of color fields have different behavior: those which are almost classical, and those which are purely quantum; (b) the second components create a gluon condensate that is a source of the field for the almost classical components of the Proca field; (c) Proca masses may appear as a result of an approximate description of the gluon condensate; (d) the question of gauge invariance is considered. It is shown that the results obtained are in good agreement with the results of lattice calculations. We make an assumption that an approximate description of a flux tube in quantum chromodynamics can be carried out using classical Proca equations but with a mandatory account of a gluon condensate.

Runaway Gravitational Production of Dark Photons.

We demonstrate that gravitational particle production of a massive, Abelian, vector (Proca) field during inflation in the presence of nonminimal coupling to gravity may suffer from an instability which leads to runaway production of high-momentum modes. This is untenable unless there is some mechanism to regulate the runaway. We discuss the parameter space of the particle mass and nonminimal couplings where such a runaway occurs and possible ways to tame the runaway. We find that there is no obvious way to resolve the runaway in a UV completion or with kinetic mixing to the standard model.

Proca in an Expanding Universe

AbstractThe superradiant growth of massive vector fields in rotating black hole spacetimes has garnered significant attention in recent literature. However, the majority of these studies overlook the influence of a cosmological constant, which likely constitutes the primary energy content of our universe. In this paper, we extend recent research by incorporating a cosmological constant into the Einstein+Proca system and numerically evolving the resulting equations of motion. Utilizing the newly released GRBoondi numerical relativity code, designed specifically for the numerical evolution of (generalized) Proca fields, we discover that parameters causing a growing instability in the scenario transition to a decaying state when . This results in a more intriguing phenomenology. These simulations pave the way for future full Einstein+Proca simulations to explore the secular decay of the resultant cloud from gravitational emission.

ℓ -Proca stars

Initially applied to the scalar case, we extend the applicability of the multi-field generalization with angular momentum of bosonic stars to the vector case, in order to obtain new configurations that generalize the one-field spherical Proca stars. These new objects, which we call ℓ -Proca stars, arise as stationary and spherically symmetric bosonic stars solutions of the Einstein-(multi)Proca system, whose matter content is formed by an arbitrary odd number of 2ℓ+1 of complex Proca fields with the same mass, time-frequency, radial profile and angular momentum number ℓ . We analyze the system of constraint and evolution radial equations for the matter content to show the consistency of our proposal, and obtain numerically the ground states of these new solutions for the first few values of ℓ using spectral methods.

Cone holography with Neumann boundary conditions and brane-localized gauge fields

Cone holography is a codimension-n doubly holographic model, which can be interpreted as the holographic dual of edge modes on defects. The initial model of cone holography is based on mixed boundary conditions. This paper formulates cone holography with Neumann boundary conditions, where the brane-localized gauge fields play an essential role. Firstly, we illustrate the main ideas in an AdS4/CFT1 toy model. We show that the U(1) gauge field on the end-of-the-world brane can make the typical solution consistent with Neumann boundary conditions. Then, we generalize the discussions to general codimension-n cone holography by employing brane-localized p-form gauge fields. We also investigate perturbative solutions and prove the mass spectrum of Kaluza-Klein gravitons is non-negative. Furthermore, we prove that cone holography obeys holographic c-theorem. Finally, inspired by the recently proposed chiral model in AdS/BCFT, we construct another type of cone holography with Neumann boundary conditions by applying massive vector (Proca) fields on the end-of-the-world brane.

On the direct quantization of Proca gauge invariant field

In this study, we use the generalized integration constants method “GCI” [1,2] to quantize two fields with constraints. Indeed, Proca field, that describes a massive boson is studied first, based on a Lagrangian without gauge symmetry, in order to determine the necessary brackets for its canonical quantization. Then, another gauge invariant version of this field, obtained by adding an additional scalar field in the mass term, is quantized after fixing this gauge.”

FeynGrav and Recent Progress in Computational Perturbative Quantum Gravity

This article reviews recent progress in computational quantum gravity caused by the framework that efficiently computes Feynman’s rules. The framework is implemented in the FeynGrav package, which extends the functionality of the widely used FeynCalc package. FeynGrav provides all the tools to study quantum gravitational effects within the standard model. We review the framework, provide the theoretical background for the efficient computation of Feynman rules, and present the proof of its completeness. We review the derivation of Feynman rules for general relativity, Horndeski gravity, Dirac fermions, Proca field, electromagnetic field, and SU(N) Yang–Mills model. We conclude with a discussion of the current state of the FeynGrav package and discuss its further development.

The greybody factor for the monopole and odd-parity modes of the Proca field in the Schwarzschild black hole spacetimes

The greybody factor is one of the famous results of the black hole perturbation theory, which describes the transmission probability of a particle radiated by a black hole into spatial infinity. In this work, we separated the angular parts of the equations of motion and derived the radial equations for the Proca field in the Schwarzschild black hole spacetime. The radial equations for the monopole and odd-parity modes are fully decoupled in the Schrödinger-like form. We study the greybody factor by determining the rigorous bound.

Production of massive W±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W^{\\pm }$$\\end{document} bosons and fermion–antifermion pairs from vacuum in the de Sitter Universe

In this paper we study the charged electro-weak interactions in the de Sitter geometry. We develop the reduction formalism for the Proca field with the help of the solutions for the interacting fields. Perturbation theory is used for obtaining the definition of the transition amplitudes in the first order. We apply our formalism to the study of spontaneous vacuum emission of fermions, anti-fermions and W±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W^{\\pm }$$\\end{document} bosons in the expanding de Sitter universe. Our results are generalizations of the Weinberg–Salam electro-weak theory to curved space-time, in the case of W±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W^{\\pm }$$\\end{document} boson interaction with leptons. The probability and transition amplitude are found to be a quantities which depend on the Hubble parameter. Our analytical and graphical results prove that such perturbative processes are possible only for the large expansion conditions of the early Universe. The total probability and rate of transition are obtained for the case of large expansion and we use dimensional regularization for the momenta integrals. In the end we recover the Minkowski limit, where our probabilities vanish, thus confirming the well known fact that spontaneous vacuum emission of W±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W^{\\pm }$$\\end{document} bosons and fermions is forbidden in flat space-time due to energy–momentum conservation.

Averaged energy conditions for vector fields

In this work we shall obtain sufficient conditions for the appearance of singularities in gravitational theories which propagate an extra vector degree of freedom, based on the known relaxations of the singularity theorems. We study the cases of a general Proca field and a vector theory with stable self-derivative interactions. In this study we show several cases of singularities that usually would be considered as potentially singularity-free, since they violate the usual point-like energy conditions.

Primordial gravitational waves in generalized Palatini gravity

Extended Palatini gravity is the metric-affine gravity theory characterized by zero torsion, nonzero metricity and a quadratic of the antisymmetric Ricci curvature. It reduces dynamically to general relativity plus a geometric Proca field. In this work, we study imprints of the geometric Proca field on the gravitational waves. Our results show that the geometric Proca leaves significant signatures in the gravitational wave signal, and gravitational wave energy density could be large enough to be detectable by the next upgrade of the existing GW detectors. Our results, if confirmed observationally, will be an indication that the gravity could be non-Riemannian in nature.

Worldline effective field theory of inspiralling black hole binaries in presence of dark photon and axionic dark matter

We investigate the correction to the potential that gives rise to the bound orbits and radiation from non-spinning inspiralling binary black holes in a dark matter environment consisting of axion-like particles and dark photons using the techniques of Worldline Effective Field Theory. We compute the conservative dynamics up to 1PN order for gravitational, electromagnetic, and Proca fields and up to 2PN order for the scalar field. The effect of axion-electromagnetic coupling (gaγγ) arises to the conservative dynamics at 2.5PN order and the kinetic mixing constant (γ) at 1PN order. Furthermore, we calculate the radiation due to the various fields present in our theory. We find that the contribution of gaγγ to the gravitational radiation appears at N(7)LO and to the scalar radiation appears at N(5)LO. We also find that these radiative corrections due to the coupling gaγγ vanishes for any orbit confined to a plane because of the existence of a binormal like term in effective radiative action but give rise to non-zero contributions for any orbit that lies in three dimensions. Last but not the least, γ contributes to the gravitational radiation at N(2)LO and N(4)LO.

A perturbative production of massive Z bosons and fermion–antifermion pairs from the vacuum in the de Sitter Universe

In this paper we study the problem of neutral electro-weak interactions in a de Sitter geometry. We develop the formalism of reduction for the Proca field with the help of the solutions for the interacting fields and by using perturbative methods we obtain the definition of the transition amplitudes in the first order of perturbation theory. As an application to our formalism we study the generation of massive fermions and Z bosons from vacuum in the expanding de Sitter universe. Our results are the generalization to the curved geometry of the Weinberg–Salam electro-weak theory for the case of Z boson interaction with leptons. The probability is found to be a quantity that depends on the Hubble parameter and we prove that such perturbative processes are possible only for large expansion regime of the early Universe. The total probability and rate of transition are obtained for the case of large expansion and we use the dimensional regularization for extract finite results from the momenta integrals. In the Minkowski limit we obtain that the probability of particle generation from vacuum is vanishing recovering the well known result that forbids particle production in flat space-time due to the momentum-energy conservation.

Generalizations and challenges for the spacetime block-diagonalization

Discovery that gravitational field equations may coerce the spacetime metric with isometries to attain a block-diagonal form compatible with these isometries, was one of the gems built into the corpus of black hole uniqueness theorems. We revisit the geometric background of a block-diagonal metric with isometries, foliation defined by Killing vector fields and the corresponding Godbillon–Vey characteristic class. Furthermore, we analyse sufficient conditions for various matter sources, including scalar, nonlinear electromagnetic and Proca fields, that imply the isometry-compatible block-diagonal form of the metric. Finally, we generalize the theorem on the absence of null electromagnetic fields in static spacetimes to an arbitrary number of spacetime dimensions, wide class of gravitational field equations and nonlinear electromagnetic fields.

Spin supplementary condition in quantum field theory: covariant SSC and physical state projection

The spin supplementary conditions are constraints on spin degrees of freedom in classical relativity which restricts physical degrees of freedom to rotations. It is argued that the equivalent constraints in quantum field theory are the projection conditions on polarisation tensors, which remove timelike/longitudinal polarisations from the physical spectrum. The claim is supported by three examples of massive spinning particles coupled to electromagnetism: Dirac and Proca fields in quantum field theory, and \U0001d4a9 = 1 worldline QFT for classical worldline theory. This suggests a resolution to the apparent discrepancy between effective field theory description of massive higher-spin fields [1, 2] and post-Newtonian effective field theory of spinning classical particles [3], where the former admits more unfixed parameters compared to the latter; the additional parameters are fixed by projection conditions and therefore are not tunable parameters.

To Half-Be or Not To Be?

It has recently been argued that half degrees of freedom could emerge in Lorentz and parity invariant field theories, using a non-linear Proca field theory dubbed Proca-Nuevo as a specific example. We provide two proofs, using the Lagrangian and Hamiltonian pictures, that the theory possesses a pair of second class constraints, leaving D − 1 degrees of freedom in D spacetime dimensions, as befits a consistent Proca model. Our proofs are explicit and straightforward in two dimensions and we discuss how they generalize to an arbitrary number of dimensions. We also clarify why local Lorentz and parity invariant field theories cannot hold half degrees of freedom.

The Quantization of Proca Fields on Globally Hyperbolic Spacetimes: Hadamard States and Møller Operators

This paper deals with several issues concerning the algebraic quantization of the real Proca field in a globally hyperbolic spacetime and the definition and existence of Hadamard states for that field. In particular, extending previous work, we construct the so-called Møller *-isomorphism between the algebras of Proca observables on paracausally related spacetimes, proving that the pullback of these isomorphisms preserves the Hadamard property of corresponding quasifree states defined on the two spacetimes. Then, we pull back a natural Hadamard state constructed on ultrastatic spacetimes of bounded geometry, along this *-isomorphism, to obtain an Hadamard state on a general globally hyperbolic spacetime. We conclude the paper, by comparing the definition of an Hadamard state, here given in terms of wavefront set, with the one proposed by Fewster and Pfenning, which makes use of a supplementary Klein–Gordon Hadamard form. We establish an (almost) complete equivalence of the two definitions.

Probing geometric proca in metric-palatini gravity with black hole shadow and photon motion

Extended metric-Palatini gravity, quadratic in the antisymmetric part of the affine curvature, is known to lead to the general relativity plus a geometric Proca field. The geometric Proca, equivalent of the non-metricity vector in the torsion-free affine connection, qualifies to be a distinctive signature of the affine curvature. In the present work, we explore how shadow and photon motion near black holes can be used to probe the geometric Proca field. To this end, we derive static spherically symmetric field equations of this Einstein-geometric Proca theory, and show that it admits black hole solutions in asymptotically AdS background. We perform a detailed study of the optical properties and shadow of this black hole and contrast them with the observational data by considering black hole environments with and without plasma. As a useful astrophysical application, we discuss constraints on the Proca field parameters using the observed angular size of the shadow of supermassive black holes M87^* and Sgr A^* in both vacuum and plasma cases. Overall, we find that the geometric Proca can be probed via the black hole observations.

Local continuity of angular momentum and noether charge for matter in general relativity

Conservation laws have many applications in numerical relativity. However, it is not straightforward to define local conservation laws for general dynamic spacetimes due the lack of coordinate translation symmetries. In flat space, the rate of change of energy-momentum within a finite spacelike volume is equivalent to the flux integrated over the surface of this volume; for general spacetimes it is necessary to include a volume integral of a source term arising from spacetime curvature. In this work a study of continuity of matter in general relativity is extended to include angular momentum of matter and Noether currents associated with gauge symmetries. Expressions for the Noether charge and flux of complex scalar fields and complex Proca fields are found using this formalism. Expressions for the angular momentum density, flux and source are also derived which are then applied to a numerical relativity collision of boson stars in 3D with non-zero impact parameter as an illustration of the methods.