In the current paper, we construct a Lorentz-violating electrodynamics in (1+2) spacetime dimensions from the electromagnetic sector of the nonminimal Standard-Model Extension (SME) in (1+3) dimensions. Subsequently, we study some of the basic properties of this framework. We obtain the field equations, the Green's functions, and the perturbative Feynman rules. Furthermore, the modified dispersion relations are computed at leading order in Lorentz violation. We then remove the unphysical degrees of freedom from the electromagnetic Green's function that are present due to gauge invariance. The resulting object is used to construct the general solutions of the uncoupled field equations with external inhomogeneities present. This modified planar electrodynamics may be valuable to describe electromagnetic phenomena in two-dimensional condensed-matter systems. Furthermore, it supports a better understanding of the electromagnetic sector of the nonminimal SME.
This article is devoted to finding classical point-particle equivalents for the fermion sector of the nonminimal Standard-Model Extension (SME). For a series of nonminimal operators, such Lagrangians are derived at first order in Lorentz violation using the algebraic concept of Gröbner bases. Subsequently, the Lagrangians serve as a basis for reanalyzing the results of certain kinematic tests of Special Relativity that were carried out in the last century. Thereby, a number of new constraints on coefficients of the nonminimal SME is obtained. In the last part of the paper we point out connecti…
We examine a new class of CPT-even and dimension-five nonminimal interactions between fermions and photons, deprived of higher-order derivatives, yielding electric dipole moment and magnetic dipole moment in the context of the Dirac equation. These couplings are Lorentz-violating nonminimal structures, composed of a rank-2 tensor, the electromagnetic tensor, and gamma matrices, being addressed in its axial and non-axial hermitian versions. We use the electron's anomalous magnetic and electric dipole moment measurements to reach upper bounds of $1$ part in $10^{11}$ and $10^{16}$ GeV$^{-1}$.
In this work, we propose two possibilities of CPT-odd and Lorentz-violating (LV) nonminimal couplings in the Electroweak sector. These terms are gauge-invariant and couple a fixed 4-vector to the physical fields of the theory. After determining the LV contributions to the electroweak currents, we reassess the evaluation of the decay rate for the vector mediators $W$ and $Z$. Using the experimental uncertainty in these decay rates, upper bounds of $1$ part in $10^{-15}$ (eV )$^{-1}$ and $10^{-14}$ (eV )$^{-1}$ are imposed on the magnitude of the proposed nonmimal interactions.
We discuss new exact solutions of a three-parameter nonminimal Einstein-Maxwell model. The solutions describe static spherically symmetric objects with and without center, supported by an electric field nonminimally coupled to gravity. We focus on a unique one-parameter model, which admits an exact solution for a traversable electrically charged wormhole connecting two universes, one asymptotically flat the other asymptotically de Sitter ones. The relation between the asymptotic mass and charge of the wormhole and its throat radius is analyzed. The wormhole solution found is thus a nonminimal …
The relentless efforts of the physics community has not yet availed us the solution of how to unify the Quantum Mechanics with General Relativity, a puzzle that has engaged the minds of the physicists for almost a century. The insufficiency of today's and foreseeable future's technology for a direct reach into the Planck energies at which the fundamental theory, the Quantum Theory of Gravity, lies has lead to the search of the low energy effects of that fundamental Planck level theory irregardless of the details of it. In this thesis, one of the leading candidates of such an exotic effect, tha…
We consider an effective model formed by usual QED (minimal coupling) with the addition of a nonminimal Lorentz violating interaction (proportional to a fixed 4-vector $b_μ$) which may radiatively generate both CPT even and odd terms in the pure gauge sector. We show that gauge invariance from usual QED, considered as a limit of the model for $b_μ\rightarrow 0$, plays an important role in the discussion of the radiatively induced Lorentz violating terms at one-loop order. Moreover, despite the nonrenormalizability of the (effective) model preventing us from readily extending our discussion to …
This paper is dedicated to the study of interactions between external sources for the electromagnetic field in a Lorentz symmetry breaking scenario. We focus on a particular higher derivative, Lorentz violating interaction that arises from a specific model that was argued to lead to interesting effects in the low energy phenomenology of light pseudoscalars interacting with photons. The kind of higher derivative Lorentz violating interaction we discuss do not appear in the well known Standard Model Extension, therefore they are called nonminimal. They are usually expected to be relevant only at…
We provide the first step towards renormalization in a nonminimal Lorentz-violating model consisting of normal scalars and modified fermions with mass dimension five operators. We compute the radiative corrections corresponding to the scalar self-energy, and we show that some divergencies are improved and in the scalar sector they are finite. The pole mass of the scalar two-point function is found and shown to lead to modifications of asymptotic states.
This work is devoted to the construction of slowly rotating neutron stars in the framework of the nonminimal derivative coupling sector of Horndeski theory. We match the large radius expansion of spherically symmetric solutions with cosmological solutions and we find that the most viable model has only one free parameter. Then, by using several tabulated and realistic equations of state, we establish numerically the upper bound for this parameter in order to construct neutron stars in the slow rotation approximation with the maximal mass observed today. We finally study the surface redshift an…
We discuss nonminimal couplings of fermions to the electromagnetic field, which generically appear in models with extra dimensions. We consider models where the electromagnetic field is generated by the Kaluza-Klein mechanism. The nonminimal couplings contribute at tree-level to anomalous magnetic and electric dipole moments of fermions. We use recent measurements of these quantities to put limits on the parameters of models with extra dimensions.
In this letter, we examine a new class of CPT-even nonminimal interactions, between fermions and photons, deprived of higher order derivatives, that yields electric dipole moment (EDM) and magnetic dipole moment (MDM) in the context of the Dirac equation. The couplings are dimension-five CPT-even and Lorentz-violating nonminimal structures, composed of a rank-2 tensor, $T_{μν}$, the electromagnetic tensor, and gamma matrices, being addressed in its axial and non-axial Hermitian versions, and also comprising general possibilities. We then use the electron's anomalous magnetic dipole moment and …
We study an extension of QED involving a light pseudoscalar (an axion-like particle), together with a very massive fermion which has Lorentz-violating interactions with the photon and the pseudoscalar, including a nonminimal Lorentz-violating coupling. We investigate the low energy effective action for this model, after integration over the fermion field, and show that interesting results are obtained, such as the generation of a correction to the standard coupling between the axion-like particle and the photon, as well as Lorentz-violating effects in the interaction energy involving electroma…
We establish a new self-consistent system of equations accounting for a nonminimal coupling of the cooperative gravitational, electromagnetic and pseudoscalar (axion) fields in a multi-component relativistic plasma. The axionic extension of the nonminimal Einstein-Maxwell-Vlasov theory is based on two consistent procedures. First, we use the Lagrange formalism to obtain nonminimal equations for the gravitational, electromagnetic and pseudoscalar fields with the additional sources generated in plasma. Second, we use the Vlasov version of the relativistic kinetic theory of the plasma, guided by …
We consider scalar-tensor gravity with nonminimal derivative coupling and Born-Infeld electromagnetic field which is minimally coupled to gravity. Since cosmological constant is taken into account it allowed us not only derive static black hole with spherical horizon but also to obtain topological solutions with non-spherical horizons. The obtained metrics are thoroughly analyzed, namely for different distances and types of topology of horizon. To investigate singularities of the metrics Kretschmann scalar is used and it is shown that the character of singularity depends on the type of topolog…
The current paper is dedicated to determining perturbative expansions for Lagrangians describing classical, relativistic, pointlike particles subject to Lorentz violation parameterized by the nonminimal Standard-Model Extension (SME). An iterative technique recently developed and applied to a Lorentz-violating scalar field theory is now adopted to treat the spin-degenerate SME fermion sector. Lagrangians are obtained at third order in Lorentz violation for the operators $\hat{a}_μ$, $\hat{c}_μ$, $\hat{e}$, $\hat{f}$, and $\hat{m}$ for arbitrary mass dimension. The results demonstrate the impac…
Scalar-tensor theory of gravity with nonlinear electromagnetic field, minimally coupled to gravity is considered and static black hole solutions are obtained. Namely, power-law and Born-Infeld nonlinear Lagrangians for the electromagnetic field are examined. Since the cosmological constant is taken into account, it allowed us to investigate so-called topological black holes. Black hole thermodynamics is studied, in particular temperature of the black holes is calculated and examined and the first law of thermodynamics is obtained with help of Wald's approach.
Scalar and vector bosons in the background of one-dimensional nonminimal vector linear plus inversely linear potentials are explored in a unified way in the context of the Duffin-Kemmer-Petiau theory. The problem is mapped into a Sturm-Liouville problem with an effective singular oscillator. With boundary conditions emerging from the problem, exact bound-state solutions in the spin-0 sector are found in closed form and it is shown that the spectrum exhibits degeneracy. It is shown that, depending on the potential parameters, there may or may not exist bound-state solutions in the spin-1 sector…
An effective model for QED with the addition of a nonminimal coupling with a chiral character is investigated. This term, which is proportional to a fixed 4-vector $b_μ$, violates Lorentz symmetry and may originate a CPT-even Lorentz breaking term in the photon sector. It is shown that this Lorentz breaking CPT-even term is generated and that,in addition, the chiral nonminimal coupling requires this term is present from the beginning. The nonrenormalizability of the model is invoked in the discussion of this fact and the result is confronted with the one from a model with a Lorentz-violating n…
This paper is devoted to the study of interactions between stationary electromagnetic sources for the minimal and nonminimal CPT-odd photon sector of the Standard Model Extension (SME), where we search mainly for physical phenomena not present in the Maxwell electrodynamics. First we consider the minimal CPT-odd sector, where the Lorentz violation is caused by the Carroll-Field-Jackiw (CFJ) term, namely $\simε^{μναβ}\left(k_{AF}\right)_μA_νF_{αβ}$, and we treat the Lorentz breaking parameter $\left(k_{AF}\right)^μ$ perturbatively up to second order. We consider effects due to the presence of p…
We present new results for classical-particle propagation subject to Lorentz violation. Our analysis is dedicated to spin-nondegenerate operators of arbitrary mass dimension provided by the fermion sector of the Standard-Model Extension. In particular, classical Lagrangians are obtained for the operators $\hat{b}_μ$ and $\hat{H}_{μν}$ as perturbative expansions in Lorentz violation. The functional dependence of the higher-order contributions in the background fields is found to be quite peculiar, which is probably attributed to particle spin playing an essential role for these cases. This pape…
We have studied the contributions of Lorentz-violating CPT-odd and CPT-even nonminimal couplings to the energy spectrum of the mesonic hydrogen and the higher-order radiative corrections to the effective action of the photon sector of a Lorentz-violating version of the scalar electrodynamics. By considering the complex scalar field describes charged mesons (pion or kaon), the non-relativistic limit of the model allows to attain upper-bounds by analyzing its contribution to the mesonic hydrogen energy. By using the experimental data for the $1S$ strong correction shift and the pure QED transiti…
We study nonminimal extensions of Einstein-Maxwell theory with exact electromagnetic duality invariance. Any such theory involves an infinite tower of higher-derivative terms whose computation and summation usually represents a challenging problem. Despite that, we manage to obtain a closed form of the action for all the theories with a quadratic dependence on the vector field strength. In these theories we find that the Maxwell field couples to gravity through a curvature-dependent susceptibility tensor that takes a peculiar form, reminiscent of that of Born-Infeld Lagrangians. We study the s…
We derive the odd parity perturbation equation in scalar-tensor theories with a non minimal kinetic coupling sector of the general Horndeski theory, where the kinetic term is coupled to the metric and the Einstein tensor. We derive the potential of the perturbation, by identifying a master function and switching to tortoise coordinates. We then prove the mode stability under linear odd- parity perturbations of hairy black holes in this sector of Horndeski theory, when a cosmological constant term in the action is included. Finally, we comment on the existence of slowly rotating black hole solu…
In the current paper the Lagrangian of a classical, relativistic point particle is obtained whose conjugate momentum satisfies the dispersion relation of a quantum wave packet that is subject to Lorentz violation based on a particular coefficient of the nonminimal Standard-Model Extension (SME). The properties of this Lagrangian are analyzed and two corresponding Finsler structures are obtained. One structure describes a scaled Euclidean geometry, whereas the other is neither a Riemann nor a Randers or Kropina structure. The results of the article provide some initial understanding of classica…
In this letter we study the self-energy of a point-like charge for the electromagnetic field in a non minimal Lorentz symmetry breaking scenario in a $n+1$ dimensional space time. We consider two variations of a model where the Lorentz violation is caused by a background vector $d^ν$ that appears in a higher derivative interaction. We restrict our attention to the case where $d^μ$ is a time-like background vector, namely $d^{2}=d^μd_μ>0$, and we verify that the classical self-energy is finite for any odd spatial dimension $n$ and diverges for even $n$. We also make some comments regarding obst…
Neutral fermions of spin 1/2 with magnetic moment can interact with electromagnetic fields through nonminimal coupling. In 2+1 dimensions the electromagnetic field strength plays the same role to the magnetic moment as the vector potential to the electric charge. This duality enables one to obtain physical results for neutral particles from known ones for charged particles. We give the probability of neutral particle-antiparticle pair creation in the vacuum by non-uniform electromagnetic fields produced by constant uniform charge and current densities.
We investigate dimension five Lorentz-violating nonminimal interactions in the electroweak sector, in connection with the possible generation of electric dipole moment (EDM), weak electric dipole moment (WEDM), magnetic dipole moment (MDM) and weak magnetic dipole moment (WMDM) for leptons. These couplings are composed of the physical fields and LV tensors of ranks ranging from 1 to 4. The CPT-odd couplings do no generate EDM\ behavior and do not provide the correct MDM\ signature, while the CPT-even ones yield EDM and MDM\ behavior, being subject to improved constraining. Tau lepton experimen…
In the current paper the properties of a quantum field theory based on certain sets of Lorentz-violating coefficients in the nonminimal fermion sector of the Standard-Model Extension are analyzed. In particular, three families of coefficients are considered, where two of them are CPT-even and the third is CPT-odd. As a first step the modified fermion dispersion relations are obtained. Then the positive- and negative-energy solutions of the modified Dirac equation and the fermion propagator are derived. These are used to demonstrate the validity of the optical theorem at tree-level, which provi…
In this paper, we consider an electrodynamics of higher derivatives coupled to a Lorentz-violating background tensor. Specifically, we are interested in a dimension-five term of the CPT-odd sector of the nonminimal Standard-Model Extension. By a particular choice of the operator $\hat{k}_{AF}$, we obtain a higher-derivative version of the Carroll-Field-Jackiw (CFJ) term, $\frac{1}{2}ε^{κλμν}A_λD_κ\square F_{μν}$, with a Lorentz-violating background vector $D_κ$. This modification is subject to being investigated. We calculate the propagator of the theory and from its poles, we analyze the disp…
We construct an extension of f(T) gravity with the inclusion of a non-minimal torsion-matter coupling in the action. The resulting theory is a novel gravitational modification, since it is different from both f(T) gravity, as well as from the non-minimal curvature-matter-coupled theory. The cosmological application of this new theory proves to be very interesting. In particular, we obtain an effective dark energy sector whose equation-of-state parameter can be quintessence or phantom-like, or exhibit the phantom-divide crossing, while for a large range of the model parameters the Universe resu…
Various studies have already considered radiative corrections in Lorentz-violating models unveiling many instances where a minimal or nonminimal operator generates, via loop corrections, a contribution to the photon sector of the Standard-Model Extension. However, an important fraction of this literature does not follow the widely accepted conventions and notations of the Standard-Model Extension, and this obscures the comparison between different calculations as well as possible phenomenological consequences. After reviewing some of these works, we uncover one example where a well defined loo…
Recently, a state of the art experiment shows evidence for Lorentz violation in the gravitational sector. To explain this experiment, we investigate a spontaneous Lorentz violation scenario with a generalized scalar field. We find that when the scalar field is nonminimally coupled to gravity, the Lorentz violation induces a deformation in the Newtonian potential along the direction of Lorentz violation.
In the context of the nonminimal Standard-Model Extension a special subset of the CPT-even higher-dimensional operators in the photon sector is discussed from a quantum-field theoretical point of view. The modified dispersion laws, photon polarization vectors plus the gauge field propagator are obtained and their properties are analyzed. It is demonstrated that for certain sectors of the modified theory a puzzle arises for the optical theorem at tree-level. This is followed by a discussion of how it can be interpreted and resolved at first order Lorentz violation. Furthermore the commutator of…
Black bounce solutions via nonminimal scalar-electrodynamic couplings
Instituto de Astrofísica e Ciências do Espaço（天体物理学与空间科学研究所）；Faculdade de Ciências da Universidade de Lisboa（里斯本大学理学院）；Universidade Federal do Pará（帕拉联邦大学）；Universidade Federal do Sul e Sudeste do Pará（帕拉南和东南联邦大学）；Faculdade de Ciências Exatas e Tecnologia（精确科学与技术学院）
The CPT-even abelian gauge sector of the Standard Model Extension is represented by the Maxwell term supplemented by $(K_{F})_{μνρσ}F^{μν}F^{ρσ}$, where the Lorentz-violating background tensor, $(K_{F})_{μνρσ}$, possesses the symmetries of the Riemann tensor. In the present work, we examine the planar version of this theory, obtained by means of a typical dimensional reduction procedure to $(1+2)$ dimensions. The resulting planar electrodynamics is composed of a gauge sector containing six Lorentz-violating coefficients, a scalar field endowed with a noncanonical kinetic term, and a coupling t…
In this paper, based on the Standard Model Extended gauge sector, we made a non-minimal coupling in the Klein-Gordon equation which characterizes the Lorentz symmetry violation and, through this nonminimal CPT-odd coupling, we investigate the effects of possible scenarios of Lorentz symmetry violation by electrical and magnetic field configurations on a massive scalar field in this background, where, analytically, we determine solutions of bound states.
We discuss our study of QCD in the presence of CP-odd electromagnetic (e.m.) background fields. We investigate the propagation of the CP-odd term from the e.m. sector to the strong sector, inducing an effective $θ$ term. We discuss the method we have used in our lattice QCD simulations, and the results of our analysis, which are relevant to the determination of the effective pseudoscalar QED-QCD interactions. We also explore how these CP-odd e.m. background fields influence the number of the Dirac zero modes in our configurations.
We consider electromagnetic field quantization in an expanding universe. We find that the covariant (Gupta-Bleuler) method exhibits certain difficulties when trying to impose the quantum Lorenz condition on cosmological scales. We thus explore the possibility of consistently quantizing without imposing such a condition. In this case there are three physical states, which are the two transverse polarizations of the massless photon and a new massless scalar mode coming from the temporal and longitudinal components of the electromagnetic field. An explicit example in de Sitter space-time shows th…
Recently, it was suggested that there was some sort of breakdown of quantum field theory in the presence of boundaries, manifesting itself as a torque anomaly. In particular, Fulling et al. used the finite energy-momentum-stress tensor in the presence of a perfectly conducting wedge, calculated many years ago by Deutsch and Candelas, to compute the torque on one of the wedge boundaries, where the latter was cutoff by integrating the torque density down to minimum lower radius greater than zero. They observed that that torque is not equal to the negative derivative of the energy obtained by int…
The anomaly-induced effective action is a useful tool for deriving the contributions coming from quantum effects of massless conformal fields. It is well-known that such corrections in the higher derivative vacuum sector of the gravitational action provide the same exponential inflation (Starobinsky model) as the cosmological constant term. At the same time, the presence of a classical electromagnetic field breaks down the exponential solution. In this paper we explore the role of the anomaly-induced term in the radiation sector and, furthermore, derive the ``equation of state'' and the scalin…
The well-known analogy between a special limit of General Relativity and electromagnetism is explored in the context of the Lorentz-violating Standard-Model Extension (SME). An analogy is developed for the minimal SME that connects a limit of the CPT-even component of the electromagnetic sector to the gravitational sector. We show that components of the post-newtonian metric can be directly obtained from solutions to the electromagnetic sector. The method is illustrated with specific examples including static and rotating sources. Some unconventional effects that arise for Lorentz-violating el…
