Carroll Field Jackiw Research Articles

QED-vacuum response and Cherenkov radiated energy in non-linear and Lorentz-symmetry violating scenarios

We explore the physical effects of non-linear electrodynamic coupled to parameters that indicate a violation of Lorentz-symmetry breaking (LSV). To do this, we consider a general non-linear photonic Lagrangian that is coupled to the Carroll–Field–Jackiw’s model (CFJ). Our investigation reveals how the constitutive properties of the vacuum and wave propagation are affected by the interference of the parameters LSV with the specific non-linear electrodynamic model under consideration. We also analyze the refractive indices for this new medium characterized by the coupling between non-linearities and the operators that carry the LSV message. Our results show that the QED-vacuum responds with birefringence and a dispersive propagation of waves. After that, we study the electromagnetic radiation produced by a moving charged particle interacting with this new medium. Our analysis shows that the emitted radiation is similar (resembles) to that of the Cherenkov effect for certain intensities of background magnetic fields. Finally, we compute the static potential profile within the framework of the gauge-invariant, but path-dependent, variables formalism. We find a logarithmic correction to the usual static Coulomb potential stemming from the LSV parameter, and there are also corrections due to the non-linearity. However, the logarithm behavior disappears whenever the LSV parameter is switched off.

Probing the interference between non-linear, axionic and space-time-anisotropy effects in the QED vacuum

In this paper, we pursue the investigation of a generic non-linear extension of axionic electrodynamics in a Carroll-Field-Jackiw (CFJ) scenario that implements Lorentz-symmetry violation (LSV). The model we inspect consists of an arbitrary non-linear electrodynamic action coupled to the axion field in presence of an anisotropy four-vector that realizes the breaking of Lorentz symmetry under the particle point of view. For the sake of our considerations, the non-linear electromagnetic field is expanded around a constant and uniform magnetic background up to second order in the propagating photon field. The focus of our attention is the study of the material properties of the vacuum in the particular case of a space-like CFJ 4-vector. The dispersion relations associated to the plane wave solutions are explicitly worked out in two situations: the magnetic background perpendicular and parallel to the wave direction. We extend these results to consider the analysis of the birefringence phenomenon in presence of non-linearity, the axion and the LSV manifested through the spatial anisotropy. Three specific proposals of non-linear electrodynamics are contemplated: Euler-Heisenberg (EH), Born-Infeld (BI) and the Modified Maxwell electrodynamics (ModMax). Throughout the paper, we shall justify why we follow the unusual path of connecting, in a single Lagrangian density, three pieces of physics beyond the Standard Model, namely, non-linearity, axions and LSV. We anticipate that we shall not be claiming that the simultaneous introduction of these three topics beyond the Standard Model will bring new insights or clues for the efforts to detect axions or to constrain parameters associate to both non-linear electrodynamics and LSV physics. Our true goal is to actually inspect and describe how axionic, non-linear and LSV effects interfere with one another whenever physical entities like group velocity, refraction indices, birefringence and effective masses of physical excitations are computed in presence of an external constant and homogeneous magnetic field.

Material boundaries in Carroll–Field–Jackiw Lorentz-violating electrodynamics

Material boundaries in Carroll–Field–Jackiw Lorentz-violating electrodynamics

Lorentz-breaking Rarita-Schwinger model

In this paper, we formulate the simplest Lorentz-breaking extension for the spin-3/2 field theory and couple it to the Abelian gauge field in a Lorentz violating (LV) manner. Next, we calculate the lower LV quantum corrections, that is, the Carroll-Field-Jackiw (CFJ) term, which, being superficially divergent, turns out to be finite but ambiguous, and also the higher-derivative CFJ term. Besides, we compute the aether term, being the lowest CPT-even LV term, involving the second order in the LV vector.

Non-Abelian Carroll–Field–Jackiw term in a Rarita-Schwinger model

In this paper, we demonstrate the possibility of generating a non-Abelian Carroll–Field–Jackiw (CFJ) term in the theory of a non-Abelian gauge field coupled to a spin-3/2 field in the presence of the constant axial vector field. Applying two regularization schemes, we prove that this term is finite and ambiguous, particularly vanishing within the 't Hooft-Veltman scheme.

External sources in a minimal and nonminimal CPT-odd Lorentz violating Maxwell electrodynamics

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, [Formula: see text], and we treat the Lorentz breaking parameter [Formula: see text] perturbatively up to second order. We consider effects due to the presence of point-like charges, Dirac strings and point-like dipoles. In special, we calculate the electromagnetic field produced outside the string and investigate the so-called Aharonov–Bohm bound states in Lorentz violation context. Afterwards, we consider a model where the Lorentz violation is generated by the higher-derivative version of the CFJ model, namely, [Formula: see text], which is a dimension five term of the CPT-odd sector of the nonminimal SME. For this higher-derivative model, we obtain effects up to second order in [Formula: see text] related to the presence of point-like charges and a steady current line. We use overestimated constraints for the Lorentz violation parameters in order to investigate the physical relevance of some results found in atomic systems. We also make an overestimate for the background vectors using experimental data from the atomic electric field.

Generation of Carroll–Field–Jackiw term in the functional integral approach within Horava–Lifshitz z = 3 CPT-violating QED

In this paper, we apply the functional integral methodology to induce the Carroll–Field–Jackiw (CFJ) term in Horava–Lifshitz [Formula: see text] CPT-violating QED, where Lorentz and CPT breaking for fermion and photon sectors is introduced, and show that the CFJ term is finite but undetermined.

CPT-violating z = 3 Horava–Lifshitz QED and generation of the Carroll–Field–Jackiw term

We study the new extension of the [Formula: see text] Horava–Lifshitz QED involving a CPT-breaking term, characterized by the axial vector [Formula: see text], and calculate the Carroll–Field–Jackiw (CFJ) term in the one-loop approximation. Explicitly, we use two regularization schemes and demonstrate that in our case, the CFJ term is finite but ambiguous, so that its exact coefficient depends on the used regularization.

No radiative corrections to the Carroll–Field–Jackiw term beyond one-loop order

We demonstrate explicitly the absence of the quantum corrections to the Carroll–Field–Jackiw (CFJ) term beyond one-loop within the Lorentz-breaking CPT-odd extension of QED. The proof holds within two prescriptions of quantum calculations, with the axial vector in the fermion sector treated either as a perturbation or as a contribution in the exact propagator of the fermion field.

Unitarity in Stückelberg electrodynamics modified by a Carroll-Field-Jackiw term

In this work we focus on the Carroll-Field-Jackiw (CFJ) modified electrodynamics in combination with a CPT-even Lorentz-violating contribution. We add a photon mass term to the Lagrange density and study the question whether this contribution can render the theory unitary at tree-level. The analysis is based on the pole structure of the modified photon propagator as well as the validity of the optical theorem. We find, indeed, that the massive CFJ-type modification is unitary at tree-level. This result provides a further example for how a photon mass can mitigate malign behaviors.

Lorentz symmetry breaking in a Yang–Mills theory within the Gribov restriction

In this paper we take into account the existence of Gribov copies in a four-dimensional Yang–Mills theory in the Landau gauge with an effective Lorentz symmetry breaking, induced by the Carroll–Field–Jackiw (CFJ) term. The self consistent gap equation of the Gribov parameter is properly derived and, provided observational bounds to the amplitude of the CFJ parameter in the gauge theory, a qualitative analysis of the Gribov parameter and of the poles of the propagator is developed.

Maxwell electrodynamics modified by a CPT -odd dimension-five higher-derivative term

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, $\frac{1}{2}\epsilon^{\kappa\lambda\mu\nu}A_{\lambda}D_{\kappa}\square F_{\mu\nu}$, with a Lorentz-violating background vector $D_{\kappa}$. This modification is subject to being investigated. We calculate the propagator of the theory and from its poles, we analyze the dispersion relations of the isotropic and anisotropic sectors. We verify that classical causality is valid for all parameter choices, but that unitarity of the theory is generally not assured. The latter is found to break down for certain configurations of the background field and momentum. In an analog way, we also study a dimension-five anisotropic higher-derivative CFJ term, which is written as $\epsilon^{\kappa\lambda\mu\nu}A_{\lambda}T_{\kappa}(T\cdot\partial)^{2}F_{\mu\nu}$ and is directly linked to the photon sector of Myers-Pospelov theory. Within the second model, purely timelike and spacelike $T_{\kappa}$ are considered. For the timelike choice, one mode is causal, whereas the other is noncausal. Unitarity is conserved, in general, as long as the energy stays real - even for the noncausal mode. For the spacelike scenario, causality is violated when the propagation direction lies within certain regimes. However, there are particular configurations preserving unitarity and strong numerical indications exist that unitarity is guaranteed for all purely spacelike configurations. The results improve our understanding of nonminimal CPT-odd extensions of the electromagnetic sector.

Consistency of an alternative CPT-odd and Lorentz-violating extension of QED

We investigate an alternative CPT-odd Lorentz-breaking QED which includes the Carroll–Field–Jackiw (CFJ) term of the Standard Model Extension (SME), writing the gauge sector in the action in a Palatini-like form, in which the vectorial field and the field-strength tensor are treated as independent entities. Interestingly, this naturally induces a Lorentz-violating mass term in the classical action. We study physical consistency aspects of the model both at classical and quantum levels.

Induction of the Lorentz-violating effective actions in quantum electrodynamics

We introduce a Lorentz-symmetry violating extended quantum electrodynamics (QED) which preserves gauge symmetry. The extended fermionic sector can radiatively induce an extended effective action which simultaneously displays the same electromagnetic terms present in the Carroll–Field–Jackiw, Myers–Pospelov and Aether actions.

Non-analyticity of the induced Carroll-Field-Jackiw term at finite temperature

In this paper, we discuss the behavior of the Carroll-Field-Jackiw (CFJ) coefficient arising due to integration over massive fermions, and the modification suffered by its topological structure in the finite-temperature case. Our study is based on the imaginary time formalism and summation over the Matsubara frequencies. We demonstrate that the self-energy of photon is non-analytic for the small- limit, i.e., the static limit and the long-wavelength limit do not commute, while the tensorial structure of the CFJ term holds in both limits.

On the anomalies in Lorentz-breaking theories

In this paper, we discuss the chiral anomaly in a Lorentz-breaking extension of QED which, besides the common terms that are present in the Standard Model Extension, includes some dimension-five nonminimal couplings. We find, using the Fujikawa formalism, that these nonminimal couplings induce new terms in the anomaly which depend on the Lorentz-violating parameters. Perturbative calculations are also carried out in order to investigate whether new ambiguous Carroll–Field–Jackiw terms are induced in the effective action.

The gauge sector of the SME with Lorentz-symmetry violation by symplectic projector method

We propose to analyze a modified electromagnetism inspired from the gauge sector of the Standard Model extension (SME). From the point of view of a canonical formulation, we carried out the usual analysis on the constraints structure of the odd sector (Carroll–Field–Jackiw term) and a Maxwell term with an effective metric. This effective metric is obtained by a vectorial decomposition of the CPT-even term, that is absorbed in the ordinary Maxwell term. Using symplectic projector method (SPM), we obtain the dispersions relations and we have verified conditions of stability to determine the valid spectrum.

Self-dual Maxwell–Chern–Simons solitons from a Lorentz-violating model

Self-dual abelian Higgs system, involving both the Maxwell and Chern–Simons terms are obtained from Carroll–Field–Jackiw theory by dimensional reduction. Bogomolʼnyi-type equations are studied from theoretical and numerical point of view. In particular, we show that the solutions of these equations are Nielsen–Olesen vortices with electric charge.

Ultrarelativistic Bose–Einstein gas on Lorentz symmetry violation

In this paper, we study the effects of Lorentz Symmetry Breaking on the thermodynamic properties of ideal gases. Inspired by the dispersion relation coming from the Carroll–Field–Jackiw model for Electrodynamics with Lorentz and CPT violation term, we compute the thermodynamics quantities for a Boltzmann, Fermi–Dirac and Bose–Einstein distributions. Two regimes are analyzed: the large and the small Lorentz violation. In the first case, we show that the topological mass induced by the Chern–Simons term behaves as a chemical potential. For Bose–Einstein gases, a condensation in both regimes can be found.

Maxwell-Chern-Simons Models: Their Symmetries, Exact Solutions and Non-relativistic Limits

Two Maxwell-Chern-Simons (MCS) models in the (1 + 3)-dimensional space-space are discussed and families of their exact solutions are found. In contrast to the Carroll-Field-Jackiw (CFE) model [2] these systems are relativistically invariant and include the CFJ model as a particular sector.Using the InNonNu-Wigner contraction a Galilei-invariant non-relativistic limit of the systems is found, which makes possible to find a Galilean formulation of the CFJ model.