T. Mariz, R. Martinez, J. R. Nascimento, A. Yu. Petrov
In this paper, we apply the functional integral methodology to induce the Carroll-Field-Jackiw (CFJ) term in Horava-Lifshitz $z=3$ 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.
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We construct the electric and magnetic Newton-Hooke and Carroll Jackiw-Teitelboim gravity theories using the isomorphism of Newton-Hooke$_\pm$ and (A-)dS Carroll algebras in $(1+1)$-spacetime dimensions. The starting point is the non-relativistic and Carroll version of Jackiw-Teitelboim gravity without restrictions on the geometry studied in [15].
We study the $z=3$ Horava-Lifshitz QED with a CPT-breaking term, characterized by the axial vector $b_μ$, and perform the one-loop calculations. Explicitly, we demonstrate that just as in the usual Lorentz-breaking QED, in our case, the Carroll-Field-Jackiw term is finite but ambiguous.
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.
Carroll-Field-Jackiw term in a massless Rarita-Schwinger model
本研究针对无质量Rarita-Schwinger的LV QED，引入规范固定得到RS场传播子并计算Carroll-Field-Jackiw项，发现其有限且有歧义，仅在基于非线性规范框架的计算方案中结果具有规范无关性。
We show the absence of the ABJ anomaly for the Horava-Lifshitz-like QED with any even $z$. Besides of this, we study the graph contributing to the ABJ anomaly at non-zero temperature and extend the Fujikawa's methodology of studying the integral measure for our model.
In this paper, we discuss the behavior of the Carroll-Field-Jackiw (CFJ) coefficient $k^μ$ 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 $k^μ$ limit, i.e., the static limit $(k_0=0,\vec k\rightarrow 0)$ and the long wavelength limit $(k_0\rightarrow 0,\vec k= 0)$ do not commute, while the tensorial structure of the CFJ term holds …
Non-Abelian Carroll-Field-Jackiw term term in a Rarita-Schwinger model
本文证明在非阿贝尔规范场与自旋-3/2场耦合且存在恒定轴向矢量场时，可生成非阿贝尔 CFJ 项，并证明其有限且含歧义，在 't Hooft-Veltman 方案中消失。
In this work we apply different duality techniques, both the dual projection, based on the soldering formalism and the master action, in order to obtain and study the dual description of the Carroll-Field-Jackiw model \cite{cfj}, a theory with a Chern-Simons-like explicitly Lorentz and CPT violating term, including the interaction with external charges. This Maxwell-Chern-Simons-like model may be rewritten in terms of the interacting modes of a massless scalar model and a topologically massive model \cite{mcs}, that are mapped, through duality, into interacting massless Maxwell and massive sel…
We study the finite temperature properties of the Maxwell-Carroll-Field-Jackiw (MCFJ) electrodynamics for a purely spacelike background. Starting from the associated finite temperature partition function, a modified black body spectral distribution is obtained. We thus show that, if the CMB radiation is described by this model, the spectrum presents an anisotropic angular energy density distribution. We show, at leading order, that the Lorentz-breaking contributions for the Planck's radiation law and for the Stefan-Boltzmann's law are nonlinear in frequency and quadratic in temperature, respec…
In this paper we have analyzed the improved version of the Gauge Unfixing (GU) formalism of the massive Carroll-Field-Jackiw model, which breaks both the Lorentz and gauge invariances, to disclose hidden symmetries to obtain gauge invariance, the key stone of the Standard Model. In this process, as usual, we have converted this second-class system into a first-class one and we have obtained two gauge invariant models. We have verified that the Poisson brackets involving the gauge invariant variables, obtained through the GU formalism, coincide with the Dirac brackets between the original secon…
Coulomb Potential in Podolsky-Carroll-Field-Jackiw Electrodynamics
研究了波尔斯基电动力学中库仑势的特性，结合CFJ模型分析了非相对论极限下的相互作用势贡献。
Galilean Covariant Carroll--Field--Jackiw Electrodynamics
提出非相对论Carroll--Field--Jackiw理论，通过Chern--Simons型项引入外部张量破缺Galilean对称性，实现双折射现象及拓扑质量与电流的产生。
Dimensional reduction of Carroll-Field-Jackiw theory
本文通过维度约化得到伪CFJ理论，求解其静态势并证明其违反幺正性，与PQED形成对比。
Taking as a starting point a Lorentz non-invariant Abelian-Higgs model defined in 1+3 dimensions, we carry out its dimensional reduction to D=1+2, obtaining a new planar model composed by a Maxwell-Chern-Simons-Proca gauge sector, a massive scalar sector, and a mixing term (involving the fixed background (v^μ) that imposes the Lorentz violation to the reduced model. The propagators of the scalar and massive gauge field are evaluated and the corresponding dispersion relations determined. Based on the poles of the propagators, a causality and unitarity analysis is carried out at tree-level. One …
In the present work, we investigate classical solutions of the Maxwell-Carroll-Field-Jackiw-Proca (MCFJP) electrodynamics for the cases a purely timelike and spacelike Lorentz-violating (LV) background. Starting from the MCFJP Lagrangian and the associated wave equations written for the potential four-vector, the tensor form of the Green function is achieved. In the timelike case, the components of the stationary Green function are explicitly written. The classical solutions for the electric and magnetic field strengths are then evaluated, being observed that the electric sector is not modifie…
Two-loop corrections to the Carroll-Field-Jackiw term in a CPT-odd Lorentz-violating scalar QED
本文在CPT奇量子电动力学框架下系统计算了Lorentz破坏顶点的单圈修正，并确定了Carroll-Field-Jackiw项的有限双圈修正及标量场自能的紫外发散分量。
Material boundaries in Carroll-Field-Jackiw Lorentz-violating electrodynamics
本文研究了完美镜面存在下CFJ电动力学中Lorentz破坏的效应，推导了电磁场修正传播子，发现电荷靠近镜面时会出现自发力矩，并验证了特定条件下镜像法的适用性。
Carroll-Field-Jackiw term in nonlocal Lorentz-violating QED
研究非局域洛伦兹违反量子电动力学中CFJ项的辐射产生，通过全非局域形状因子引入非局域性，利用导数展开推导诱导贡献，分析紫外行为，两类形状因子分别自然收敛或经阿贝尔正则化使CFJ系数有限，为控制紫外贡献提供自然框架。
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. 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.
Cold plasma waves in the chiral Maxwell-Carroll-Field-Jackiw electrodynamics
本文在手性 Maxwell-Carroll-Field-Jackiw 电动力学框架下研究冷均匀无碰撞等离子体中的波传播与吸收，推导出四种折射率及其对应的圆偏振模式，并揭示了负折射增强旋光本领及旋光符号反转等现象。
Anisotropic cold plasma modes in chiral vector Maxwell-Carroll-Field-Jackiw electrodynamics
本研究在手性矢量MCFJ电动力学中，通过冷等离子体模型解析了各向异性等离子体波的传播与吸收，确定了RCP和LCP模式及折射率，并揭示了双折射、二向色性及旋光符号反转等手性光学效应。
Carroll dilaton supergravity in two dimensions
本文构造并讨论了二维N=1和N=2 Carroll膨胀子超引力，将其应用于超对称Carroll-Jackiw-Teitelboim模型并探讨边界条件，发现N=2版本存在“民主”与“专制”两种形式。
We write down an $\mathcal{N}=1$ supersymmetric extension for non-Abelian gauge theories in (1+3) dimensions with a Lorentz- and CPT-violating term of the Carroll-Field-Jackiw type. By including effects of the background (supersymmetric) fermion bilinears that accompany Lorentz-symmetry violation in a Carroll-Field-Jackiw scenario, we investigate both the gauge boson and gaugino dispersion relations in order to compute their respective masses in terms of the background structures. Such results open up a potential path towards a possible mechanism for gaugino-gauge boson conversion, an analogue…
In this paper, we describe the perturbative generation of the higher-derivative Lorentz-breaking terms for the gauge field, that is, the Myers-Pospelov term and the higher-derivative Carroll-Field-Jackiw term. These terms are explicitly calculated in the one-loop approximation and shown to be finite and ambiguous.
In this paper we discuss finiteness and ambiguities of the higher-derivative Lorentz-breaking terms in extended QED with a magnetic coupling at the finite temperature. We find that, beside of the higher-derivative Carroll-Field-Jackiw-like term and Myers-Pospelov term, many new terms arise in a finite temperature case, but most of them vanish in high temperature limit.
We consider the two-point function of the gauge field in Lorentz-breaking theories with higher-derivative extension of the Dirac Lagrangian. We show that the Carroll-Field-Jackiw term naturally arises in this theory as a quantum correction being perfectly finite and thus displaying no ambiguities. Also, the finiteness of this term at low energy limit and the absence of large Lorentz violating corrections allows to avoid the fine-tuning problem.
We investigate a Lorentz-violating chiral model composed by two fermions, a complex scalar field and a gauge field. We show that by convenientely adjusting the parameters of the model, it is possible to generate an unambiguous Carroll-Field-Jackiw term and, at the same time, provide the cancelation of the chiral anomaly. The renormalizability of the model is investigated and it is shown that the same counterterms needed in the symmetric phase also renormalize the model with broken symmetry.
Lorentz and CPT violating QED with massless fermions at finite temperature is studied. We show that there is no ambiguity in the induced coefficient of the Chern-Simons-like term that defines the so-called Carroll-Field-Jackiw model at high temperature. We also show that this system constitutes an example where the breaking of CPT and Lorentz symmetries is more severe at high temperature than in the zero temperature case thus precluding any naive expectations of Lorentz symmetry restoration.
We consider the Lorentz-violating extended QED involving all nonminimal dimension-5 additive CPT-odd terms. For this theory, we investigate the possibility of generating the Carroll-Field-Jackiw (CFJ) term of the first order in any of these nonminimal couplings. This term is demonstrated to vanish in certain regularization schemes. We also study the question of higher-derivative divergent contributions and demonstrate that they can be eliminated by considering a given proportionality between the coefficients.
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 $SU(2)$ gauge theory, a qualitative analysis of the Gribov parameter and of the poles of the propagator is developed.
We investigate new aspects related to the abelian gauge-Higgs model with the addition of the Carroll-Field-Jackiw term. We focus on one-loop quantum corrections to the photon and Higgs sectors due to spontaneous breaking of gauge symmetry and show that new finite and definite Lorentz-breaking terms are induced. Specifically in the gauge sector, a CPT-even aether term is induced. Besides, aspects of the one-loop renormalization of the background vector dependent terms are discussed.
We analyze the Carroll-Field-Jackiw (CFJ) modification of electrodynamics reformulated as the ordinary Maxwell theory with an additional special axion field. In this form, the CFJ model appears as a special case of the pre-metric approach recently developed by Hehl and Obukhov. This embedding turns out to be non-trivial. Particularly, the pre-metric energy-momentum tensor does not depend on the axion. This is in contrast to the CFJ energy-momentum tensor which involves the axion addition explicitly. We show that the relation between these two quantities is similar to the correspondence between…
On perturbative aspects of a nonminimal Lorentz-violating QED with CPT-odd dimension-6 terms
本文研究非最小CPT奇宇称维度6洛伦兹破缺项的单圈量子修正，证明类CFJ项可发散，但在特定参数关系下发散消除。
Lorentz-breaking Rarita-Schwinger model
本文构造了自旋-3/2场的洛伦兹破缺扩展并耦合到阿贝尔规范场，计算了有限但歧义的CFJ项、高阶导数CFJ项以及二阶LV矢量的aether项。
We have studied BPS vortices in a CPT-odd and Lorentz-violating Maxwell-Chern-Simons-Higgs (MCSH) electrodynamics attained from the dimensional reduction of the Carroll-Field-Jackiw-Higgs model. The Lorentz-violating parameter induces a pronounced behavior at origin (for the magnetic/electric fields and energy density) which is absent in the MCSH vortices. For some combination of the Lorentz-violating coefficients there always exist a sufficiently large winding number $n_{0}$ such that for all $% |n|\geq |n_{0}|$ the magnetic field flips its signal, yielding two well defined regions with oppos…
Ambiguities in the generation of CFJ-terms in a QED with dimension-5 operators in one loop
本文探讨了在包含维度5算子的QED中，一阶循环中CFJ项生成的正则化歧义问题，指出表面项在满足对称性恒等式时仍不确定，强调了正则化处理的重要性。
We take as starting point the planar model arising from the dimensional reduction of the Maxwell Electrodynamics with the (Lorentz-violating) Carroll-Field-Jackiw term. We then write and study the extended Maxwell equations and the corresponding wave equations for the potentials. The solution to these equations show some interesting deviations from the usual MCS Electrodynamics, with background-dependent correction terms. In the case of a time-like background, the correction terms dominate over the MCS sector in the region far from the origin, and establish the behaviour of a massless Electrod…
Lorentz violation through a radiatively induced Chern-Simons-like term in a fermionic theory embedded in linearized quantum gravity with a Lorentz- and CPT-violating axial-vector term in the fermionic sector proportional to a constant field $b_μ$ has been recently studied. In a similar fashion as for the extended-QED model of Carroll-Field-Jackiw, we explicitly show that neither gauge invariance nor the more stringent momentum routing invariance condition on underlying Feynman diagrams fix the arbitrariness inherent to such induced term at one loop order. We present the calculation in a nonper…
We study the spectrum of the minimal supersymmetric extension of the Carroll-Field-Jackiw model for Electrodynamics with a topological Chern-Simons-like Lorentz-symmetry violating term. We identify a number of independent background fermion condensates, work out the gaugino dispersion relation and propose a photonic effective action to consider aspects of confinement induced by the SUSY background fermion condensates, which also appear to signal Lorentz-symmetry violation in the photino sector of the action. Our calculations of the static potential are carried out within the framework of the g…
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.
In the presence of an external magnetic field, the Carroll-Field-Jackiw term introduces a displacement current proportional to the Lorentz-violating background that induces a time-dependent magnetic field. Axion-like particles or hidden photons could generate an analogous signal, potentially detectable with the set-up suggested by Sikivie, Tanner and Sullivan - a sensitive magnetometer coupled to a superconducting LC circuit. We show that a similar set-up, but with an externally driven pick-up loop whose area varies harmonically at $\sim$ Hz, can be used to probe the spatial components of the …
Lorentz-violating electrodynamics in continuous matter
该研究综述存在洛伦兹破缺项时电磁波在连续介质中的传播，讨论了含手征磁效应的电介质的经典电动力学（MCFJ理论建模），分析了不同质量维度CPT破缺项的影响及双折射、吸收现象，为经典场论与介质光学效应的相互作用提供新见解。
Perturbative Analysis of CPT-Odd Lorentz-Violating Scalar QCD
本文通过一阶微扰分析，研究了带有伴随标量物质的CPT奇反对称洛伦兹破坏标量QCD的紫外发散部分，揭示了 gauge 部分的Carroll-Field-Jackiw型修正及标量部分的CPT奇反对称单导数项，并证明了理论的乘法可重整性。
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…
Quark sector effects and glueball mass sensitivity estimates in Lorentz-violating supersymmetric QCD-like theories
该研究探讨了在洛伦兹破坏超对称QCD-like理论中，夸克部分对胶球质量敏感性的影响，并提供了拓扑质量标度的参数估计。
Considerations on electromagnetic radiation in Podolsky electrodynamics within a Lorentz-symmetry violating framework
本研究在洛伦兹对称性破缺框架下，分析耦合CFJ模型的Podolsky电动力学中高阶导数项的影响，揭示真空新特性与模式振荡机制，发现带电粒子辐射呈类切伦科夫效应分布。
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…
Field sources in a planar anisotropic CPT-odd gauge model
本文从Carroll-Field-Jackiw模型降维得到(2+1)维CPT-奇规范模型，研究了静态点源在平面电动力学中引起的洛伦兹破坏效应，并获得了背景矢量至二阶的微扰效应。
Lorentz-violating QED inspired superconductivity
研究洛伦兹破缺启发的超导金兹堡-朗道模型，引入CPT奇项，发现小项时呈迈斯纳态，大项时出现强面内电流和异常涡旋，可解释UTe₂等分层超导态。
QED-vacuum response and Cherenkov radiated energy in non-linear and Lorentz-symmetry violating scenarios
本文研究了与洛伦兹对称性破坏参数耦合的非线性电动力学，揭示了QED真空的双折射与色散响应，探讨了带电粒子在特定背景磁场下的切伦科夫辐射特征，并发现LSV参数对静态库仑势引入了对数修正。
In this work we study how CPT-odd Maxwell-Carroll-Field-Jackiw (MCFJ) electrodynamics as well as a dimension-5 extension of it affect the optical activity of continuous media. The starting point is dimension-3 MCFJ electrodynamics in matter whose modified Maxwell equations, permittivity tensor, and dispersion relations are recapitulated. Corresponding refractive indices are achieved in terms of the frequency and the vector-valued background field. For a purely timelike background, the refractive indices are real. Their associated propagation modes are circularly polarized and exhibit birefring…
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…
Probing the interference between non-linear, axionic and space-time-anisotropy effects in the QED vacuum
本文在Carroll-Field-Jackiw洛伦兹破缺场景下构建非线性轴子电动力学模型，研究恒定磁背景中真空色散关系与双折射，揭示非线性、轴子与空间各向异性效应的相互干涉。
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