T. Mariz, J. R. Nascimento, A. Yu. Petrov
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.
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The first one-loop higher-derivative contribution to the effective action of the Lorentz-breaking spinor QED is obtained and shown to be finite and ambiguous.
The origin of the radiatively induced Lorentz and CPT violations, in perturbative evaluations, of an extended version of QED, is investigated. Using a very general calculational method, concerning the manipulations and calculations involving divergent amplitudes, we clearly identify the possible sources of contributions for the violating terms. We show that consistency in the perturbative calculations, in a broader sense, leaves no room for the existence of radiatively induced contributions which is in accordance with what was previously conjectured and recently advocated by some authors suppo…
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 calculate by the method of dimensional regularization and derivative expansion the one-loop effective action for a Dirac fermion with a Lorentz-violating and CPT-odd kinetic term in the background of a gauge field. We show that this term induces a Chern-Simons modification to Maxwell theory. Some related issues are also discussed.
We speculate on Dyson series for the $S$-matrix when the interaction depends on derivatives of the fields. We stick on two particular examples: the scalar electrodynamics and the renormalised $ϕ^4$ theory. We eventually give evidence that Lorentz invariance is satisfied and that usual Feynman rules can be applied to the interaction Lagrangian.
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.
In this work, we analyze a gravity model with higher derivatives including a CPT-even Lorentz-violating term. In principle, the model could be a low-energy limit of a Lorentz-invariant theory presenting the violation of Lorentz symmetry as a consequence of a spontaneous symmetry-breaking mechanism if a decoupling between the metric and the Nambu-Goldstone modes is assumed. We have set up a convenient operator basis for the expansion of wave operators for symmetric second-rank tensors in the presence of a background vector. By using this set of operators, the particle content is obtained, and i…
We consider the higher-derivative Lorentz-breaking extension of QED, where the new terms are the Myers-Pospelov-like ones in gauge and spinor sectors, and the higher--derivative CFJ term. For this theory, we study its tree-level dynamics, discuss the dispersion relation, and present one more scheme for its perturbative generation, including the finite temperature case. Also, we develop a method to study perturbative unitarity based on consistent rotation of the theory to Euclidean space. We use this method to verify explicitly that for special choices of the Lorentz-breaking vector, the unitar…
Perturbative Aspects of CPT-Even Lorentz-Violating Scalar Chromodynamics
本文构建任意非阿贝尔规范群下的洛伦兹破缺标量QCD，并在最低阶计算发散量子修正与β函数，证明耦合满足特定关系时洛伦兹破缺部分尺度不变。
We study the problem of decoupling of heavy chiral superfields in four-dimensional $N=1$ supersymmetric field theories with Lorentz-invariant and Lorentz-violating higher-derivative terms. We demonstrate that the earlier found effect of large logarithmic quantum corrections, due to heavy chiral superfields, takes place not only if the theory possesses quantum divergences, but also for essentially finite theories involving higher derivative terms, both Lorentz-invariant and Lorentz-breaking ones.
Scalar QED is studied with higher order derivatives for the scalar field kinetic energy. A local potential is generated for the gauge field due to the covariant derivatives and the vacuum with non-vanishing expectation value for the scalar field and the vector potential is constructed in the leading order saddle point expansion. This vacuum breaks the global gauge and Lorentz symmetry spontaneously. The unitarity of time evolution is assured in the physical, positive norm subspace and the linearized equations of motion are calculated. Goldstone theorem always keeps the radiation field massless…
In this work, we analyze the generation of the higher-derivative Lorentz-violating Chern-Simons term at zero temperature and at finite temperature. We use the method of derivative expansion and the Matsubara formalism in order to consider the finite temperature effects. The results show that at zero temperature the induced higher-derivative Chern-Simons term is nonzero; in contrast, when the temperature reaches infinity, the coefficients of the induced term vanish. In addition, we also briefly study the question of large gauge invariance of this higher-derivative term as we as the conventional…
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.
On perturbative aspects of a nonminimal Lorentz-violating QED with CPT-even dimension-5 terms
该研究在含全部 CPT 偶维数 5 算符的非最小洛伦兹破缺旋量 QED 中，计算参数可由单一常矢量表示时的较低阶 CPT 偶单圈量子修正。
We determine the effect of Lorentz invariance violation in the vacuum energy and stress between two parallel plates separated by a distance $L$, in the presence of a massive real scalar field. We parametrize the Lorentz-violation in terms of a symmetric tensor $h^{\,μν}$ that represents a constant background. Through the Green's function method, we obtain the global Casimir energy, the Casimir force between the plates and the energy density in a closed analytical form without resorting to perturbative methods. With regards to the pressure, we find that $\mathcal{F}_c(L)=\mathcal{F}_0(\tilde{L}…
We study the radiatively induced Lorentz-violating terms at finite temperature, namely, the higher-derivative term and the Chern-Simons term. These terms are induced by integrating out the fermions coupled to the coefficient $g^{κμν}$. The calculation of the resulting expressions is performed by using the derivative expansion and the Matsubara formalism. The Chern-Simons terms is nonzero only at finite temperature, whereas the higher-derivative term is finite at zero temperature, however, it goes to zero as the temperature grows to infinity. We also obtain a higher-derivative Chern-Simons term…
We study the perturbative generation of higher-derivative operators as corrections to the photon effective action, which are originated from a Lorentz violation background. Such corrections are obtained, at one-loop order, through the proper-time method, using the zeta function regularization. We focus over the lowest order corrections and investigate their influence in the propagation of electromagnetic waves through the vacuum, in the presence of a strong, constant magnetic field. This is a setting of experimental relevance, since it bases active efforts to measure non linear electromagnetic…
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。
On global vortices in the higher derivative Lorentz-violating scenario
本文研究（2,1）维高阶导数洛伦兹破缺模型中全局涡旋的能量正规化，发现LIV背景不影响中性结构，但会使带电结构电场出现由LIV参数控制的特征信号，并得到有限能量的一阶解。
This paper is devoted to study the thermal aspects of a photon gas within the context of Planck-scale-modified dispersion relations. We study the spectrum of radiation and the correction to the \textit{Stefan$-$Boltzmann} law in different cases when the Lorentz symmetry is no longer preserved. Explicitly, we examine two models within the context of CPT$-$even and CPT$-$odd sectors respectively. To do so, three distinct scenarios of the Universe are considered: the Cosmic Microwave Background (CMB), the electroweak epoch, and the inflationary era. Moreover, the equations of state in these cases…
The definition of ``Lie derivative'' of spinors with respect to Killing vectors is extended to all kinds of Lorentz tensors. This Lie-Lorentz derivative appears naturally in the commutator of two supersymmetry transformations generated by Killing spinors and vanishes for Vielbeins. It can be identified as the generator of the action of isometries on supergravity fields and its use for the calculation of supersymmetry algebras is revised and extended.
We analyse the perturbative four-point amplitudes in the simplest string theory examples of T-fold backgrounds, which enjoy N=6 supersymmetries in four dimensions. There are two theories defined as asymmetric orbifolds of order 2 and 3, respectively. The perturbative spectrum and the one-loop four-point amplitudes are shown to be invariant under an arithmetic symplectic group defined over the Hurwitz (respectively Eisenstein) quaternions. The supersymmetry constraints on the low energy effective couplings are determined and we conjecture the U-duality group of the theory and the non-perturbati…
We analyze the role of Lorentz symmetry in the perturbative non-gravitational anomalies for a single family of fermions. The theory is assumed to be translational invariant, power-counting renormalizable and based on a local action, but is allowed to have general Lorentz violating operators. We study the conservation of global and gauge currents associate with general internal symmetry groups and find, by using a perturbative approach, that Lorentz symmetry does not participate in the clash of symmetries that leads to the anomalies. We first analyze the triangle graphs and prove that there are…
Higher derivative asymptotic charges and internal Lorentz symmetries
本文研究高导数渐近引力荷，揭示高导数 BMS 荷与两导数 BMS 荷的关联，并阐明内部 Lorentz 变换在高导数情形中的作用及相应荷。
We consider the abelian vector-field models in the presence of the Wess-Zumino interaction with the pseudoscalar matter. The occurence of the dynamic breaking of Lorentz symmetry at classical and one-loop level is described for massless and massive vector fields. This phenomenon appears to be the non-perturbative counterpart of the perturbative renormalizability and/or unitarity breaking in the chiral gauge theories.
We extend the perturbative approach developed in an earlier work to deal with Lagrangians which have arbitrary higher order time derivative terms for both bosons and fermions. This approach enables us to find an effective Lagrangian with only first time derivatives order by order in the coupling constant. As in the pure bosonic case, to the first order, the quantized Hamiltonian is bounded from below whenever the potential is. We show in the example of a single complex fermion that higher derivative interactions result in an effective mass and change of vacuum for the low energy modes. The sup…
We extend the notion of self-duality to spaces built from a set of representations of the Lorentz group with bosonic or fermionic behaviour, not having the traditional spin-one upper-bound of super Minkowski space. The generalized derivative vector fields on such superspaces are assumed to form a superalgebra. Introducing corresponding gauge potentials and hence covariant derivatives and curvatures, we define generalized self-duality as the Lorentz covariant vanishing of certain irreducible parts of the curvatures.
The first higher derivative term of the photon sector of Lorentz-violating QED, with operator of mass dimension $d=5$, is radiatively induced from the fermion sector, in which contains a derivative term with the dimensionless coefficient $g^{λμν}$. The calculation is performed perturbatively in the coefficient for Lorentz violation, and due to the fact that the contributions are quadratically divergent, we adopt dimensional regularization.
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。
One kind of spontaneous (2+1)-dimensional Lorentz symmetry breaking is discussed. The symmetry breaking pattern is $SO(2,1)\rightarrow SO(1,1)$. Using the coset construction formalism, we derive the Goldstone covariant derivative and the associated covariant gauge field. Finally, the two-derivative low-energy effective action of the Nambu-Goldstone bosons is obtained.
Magnetic Casimir effect of a Lorentz-violating scalar with higher order derivatives
本研究针对含高阶导数耦合类空矢量的CPT偶洛伦兹破缺带电有质量标量场，用zeta函数技术分析垂直平板磁场下两种边界条件、两种矢量方向的卡西米尔效应，得到三类渐近极限下的解析结果。
The derivative expansion of the effective action is a perturbative development in derivatives of the fields. The expansion breaks down when some of the derivatives are too large. We show how to sum exactly the first and second derivatives and treat perturbatively derivatives higher than second.
In this paper, we investigate an electrodynamics in which the physical modes are coupled to a Lorentz-violating (LV) background by means of a higher-derivative term. We analyze the modes associated with the dispersion relations (DRs) obtained from the poles of the propagator. More specifically, we study Maxwell's electrodynamics modified by a LV operator of mass dimension 6. The modification has the form ${D_{βα}}\partial_σF^{σβ}\partial_λ F^{λα}$, i.e., it possesses two additional derivatives coupled to a \textit{CPT}-even tensor $D_{βα}$ that plays the role of the fixed background. We first …
We classify the unitary, renormalizable, Lorentz violating quantum field theories of interacting scalars and fermions, obtained improving the behavior of Feynman diagrams by means of higher space derivatives. Higher time derivatives are not generated by renormalization. Renormalizability is ensured by a "weighted power counting" criterion. The theories contain a dimensionful parameter, yet a set of models are classically invariant under a weighted scale transformation, which is anomalous at the quantum level. Formulas for the weighted trace anomaly are derived. The renormalization-group proper…
We consider an extended QED with the addition of a dimension-five Lorentz-breaking coupling between spinor and gauge fields, involving a pseudo-tensor $κ^{μνλρ}$. The specific form of the Lorentz violating coupling considered by us have been suggested in other works, and some of its consequences at the classical level were already studied. Here, we investigate the consequences of this specific form of Lorentz violation at the quantum level, evaluating the one loop corrections to the gauge field two-point function, both at zero and at finite temperature. We relate the terms that are generated b…
Finite temperature Casimir effect of a Lorentz-violating scalar with higher order derivatives
本文研究了在有限温度下，洛伦兹违反标量场在平行平板间产生的Casimir效应，通过分析不同边界条件和方向下的能量与压力，得出了三种渐近极限下的解析表达式。
We construct local, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. They contain higher space derivatives, which improve the behavior of propagators at large momenta, but no higher time derivatives. We show that the regularity of the gauge-field propagator privileges a particular spacetime breaking, the one into into space and time. We then concentrate on the simplest class of models, study four dimensional examples and discuss a number of issues that arise in our approach, such as the low-energy recovery of Lo…
In this paper, we consider the perturbative generation of the CPT-even aether-like Lorentz-breaking term in the extended Lorentz-breaking QED within different approaches and discuss its ambiguities.
In this paper, we formulate a theory of the second-rank antisymmetric (pseudo)tensor field minimally coupled to a spinor, calculate the one-loop effective potential of the (pseudo)tensor field, and, explicitly, demonstrate that it is positively defined and possesses a continuous set of minima, both for tensor and pseudotensor cases. Therefore, our model turns out to display the dynamical Lorentz symmetry breaking. We also argue that, contrarily to the derivative coupling we use here, derivative-free couplings of the antisymmetric tensor field to a spinor do not generate the positively defined …
In this work we have used a Hořava-Lifshitz scaling to rewrite a Lorentz-violating higher-order derivative electrodynamics controlled by a background four-vector $n_μ$. The photon propagator was obtained and we have analyzed the dispersion relation and the observational results of gamma-ray burst (GRB) experiments were used. The limits of the critical exponent were discussed in the light of the GRB data and the physical implications were compared with the current GRB-Lorentz-invariance-violation literature. We show that the bound for the Lorentz-violating coupling for dimension-six operators, …
We review a perturbative approach to deal with Lagrangians with higher or infinite order time derivatives. It enables us to construct a consistent Poisson structure and Hamiltonian with only first time derivatives order by order in coupling. To the lowest order, the Hamiltonian is bounded from below whenever the potential is. We consider spacetime noncommutative field theory as an example.
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…
In this book, we review various aspects of the Lorentz symmetry breaking, both classical and quantum ones, with the special interest to perturbative generation of Lorentz-breaking terms. We present impacts of Lorentz symmetry breaking in noncommutative and supersymmetric theories. Also, we discuss the problem of Lorentz symmetry breaking in a curved space-time. The book is closed with a review of experimental studies of Lorentz symmetry breaking.
Bosonic Casimir effect in an aether-like Lorentz-violating scenario with higher order derivatives
研究高阶导数类以太洛伦兹破缺下玻色子卡西米尔效应，修正克莱因-戈登方程，发现能量压力修正依赖导数阶数、矢量方向及边界条件。
In a perturbative approach Einstein-Hilbert gravity is quantized about a flat background. In order to render the model power counting renormalizable, higher order curvature terms are added to the action. They serve as Pauli-Villars type regulators and require an expansion in the number of fields in addition to the standard expansion in the number of loops. Renormalization is then performed within the BPHZL scheme, which provides the action principle to construct the Slavnov-Taylor identity and invariant differential operators. The final physical state space of the Einstein-Hilbert theory is re…
Models with higher order derivative terms in the kinetic energy appear not only as effective theories, they can be considered as elementary, renormalizable models in their own right. The extension of Higgs mechanism is discussed for Yang-Mills-Higgs models where the kinetic energy of the scalar field contains higher order derivatives. The connection term of the covariant derivatives generates a local potential for the gauge field in the phase with spontaneously broken global gauge symmetry which may break Lorentz symmetry in the vacuum. Relativistic, massless gauge bosons spectrum is found for…
Using the method of perturbative quantization in the first order approximation, we quantize a non-local QED-like theory including fermions and bosons whose interactions are described by terms containing higher order space-time derivatives. As an example, the two-dimensional space-time noncommutative QED (NC-QED) is quantized perturbatively up to O(e^2,θ^3), where e is the NC-QED coupling constant and θis the noncommutativity parameter. The resulting modified Lagrangian density is shown to include terms consisting of first order time-derivative and higher order space-derivatives of the modified…
It has been argued that a certain large $N$ matrix model may provide a non-perturbative definition of $M$-theory. This model is the truncation to $0+1$ dimensions of ten-dimensional supersymmetric Yang-Mills theory. It is crucial to this identification that terms with four derivatives in the effective action for the quantum mechanics should not be renormalized. We offer a perturbative proof of this result.
The four dimensional Lorentz-breaking finite and determined Chern-Simons like action is generated as a one loop perturbative correction via an appropriate Lorentz-breaking coupling of the gauge field with the spinor field. Unlike the known schemes of calculations, within this scheme this term is found to be regularization independent.
Higher-order effects of CPT and Lorentz violation within the SME effective framework including Myers-Pospelov dimension-five operator terms are studied. The model is canonically quantized by giving special attention to the arising of indefinite-metric states or ghosts in an indefinite Fock space. As is well-known, without a perturbative treatment that avoids the propagation of ghost modes or any other approximation, one has to face the question of whether unitarity and microcausality are preserved. In this work, we study both possible issues. We found that microcausality is preserved due to th…
High-order spatial derivatives are of crucial importance for constructing the low energy effective action of a Lorentz or parity violating theory of quantum gravity. One example is the Hořava-Lifshitz gravity, in one has to consider at least the sixth-order spatial derivatives in the gravitational action, in order to make the theory power-counting renormalizable. In this paper, we consider the Lorentz and parity violating effects on the propagation of GWs due to the fifth and sixth-order spatial derivatives respectively. For this purpose we calculate the corresponding Lorentz and parity violat…
We study perturbative unitarity in the scalar sector of the Myers-Pospelov model. The model introduces a preferred four-vector $n$ which breaks Lorentz symmetry and couples to a five-dimension operator. When the preferred four-vector is chosen in the pure timelike or lightlike direction, the model becomes a higher time derivative theory, leading to a cubic dispersion relation. Two of the poles are shown to be perturbatively connected to the standard ones, while a third pole, which we call the Lee-Wick-like pole, is associated to a negative metric, in Hilbert space, threatening the preservation…
The non-minimal pure spinor formalism for the superstring is used to prove two new multiloop theorems which are related to recent higher-derivative $R^4$ conjectures of Green, Russo and Vanhove. The first theorem states that when $0<n<12$, $\partial^n R^4$ terms in the Type II effective action do not receive perturbative contributions above $n/2$ loops. The second theorem states that when $n\leq 8$, perturbative contributions to $\partial^n R^4$ terms in the IIA and IIB effective actions coincide.
One-loop contributions in Lorentz-violating scalar QED with nonminimal coupling
研究含维度五CPT奇非最小耦合的洛伦兹破坏标量QED的单圈两点函数，通过广义协变导数定义模型，计算真空极化和标量自能的发散部分，验证规范不变性。
All quadratic translation- and gauge-invariant photon operators for Lorentz breakdown are included into the Stueckelberg Lagrangian for massive photons in a generalized ξ-gauge. The corresponding dispersion relation and tree-level propagator are determined exactly, and some leading-order results are derived. The question of how to include such Lorentz-violating effects into a perturbative quantum-field expansion is addressed. Applications of these results within Lorentz-breaking quantum field theories include the regularization of infrared divergences as well as the free propagation of massive…
Quasi-Riemannian theories of gravity have smaller gauge groups acting on the tangent spacetime than the full Lorentz group. Among others, the spatial rotation group can be gauged to obtain spacetime asymmetric gravity with general covariance. We may introduce `spatial' higher-derivative interactions exclusively to improve ultraviolet behavior with unitarity.
A Lorentz non-invariant higher derivative effective action in flat spacetime, characterised by a constant vector, can be made invariant under infinitesimal Lorentz transformations by restricting the allowed field configurations. These restricted fields are defined as functions of the background vector in such a way that background dependance of the dynamics of the physical system is no longer manifest. We show here that they also provide a field basis for the realisation of Lorentz algebra and allow the construction of a Poincaré invariant symplectic two form on the covariant phase space of th…
On the consistency of Lorentz-Violating Yang-Mills theories: Gauge invariance and non-perturbative effects
针对洛伦兹破缺杨-米尔斯理论，提出含规范不变质量项的模型以解决规范依赖问题，并给出线性协变规范下精炼Gribov-Zwanziger作用的BRST不变表述，从而在微扰框架内获取红外性质。
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…
A four-dimensional Lorentz-breaking non-Abelian Chern-Simons like action is generated as a one-loop perturbative correction via an appropriate Lorentz-breaking coupling of the non-Abelian gauge field to the spinor field. This term is shown to be regularization dependent but nevertheless it can be found unambiguously in different regularization schemes at zero and finite temperature.
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