We compute, both explicitly up to next-to-leading order and in a proof by induction for all loop levels, the critical exponents for thermal Lorentz-violating O($N$) self-interacting scalar field theory. They are evaluated in a massless theory renormalized at arbitrary external momenta, where a reduced number of Feynman diagrams is eeded. The results are presented and shown to be identical to that found previously in distinct theories renormalized at different renormalization schemes. At the end we give both mathematical explanation and physical interpretation for them based on coordinates redefinition techniques and symmetry ideas, respectively.
In this work, we compute analytically the infrared divergences of massless O($N$) self-interacting scalar field theories with Lorentz violation, which are exact in the Lorentz-violating $K_{μν}$ coefficients, for evaluating the corresponding next-to-leading order critical exponents. For that, we apply three distinct and independent field-theoretic renormalization group methods. We find that the outcomes for the critical exponents are the same in the three methods and, furthermore, are identical to their Lorentz invariant counterparts. We generalize the results for all loop levels by employing …
We examine the influence of exact Lorentz-violating symmetry mechanism on the radiative quantum corrections to the critical exponents for massless $q$-deformed O($N$) $λϕ^{4}$ scalar field theories. For that, we employ three different and independent field-theoretic renormalization group methods for computing analytically the $q$-deformed critical exponents up to next-to-leading order. Then we generalize the former finite loop level results for any loop order. We show that the Lorentz-violating $q$-deformed critical exponents, obtained through the three methods, turn out to be identical and fu…
In this work we evaluate the $γ_{m}$ function corresponding to mass renormalization for O($N$) scalar field theory with Lorentz violation. We calculate this function up to two-loop order for a theory renormalized utilizing the counterterm method in the minimal subtraction scheme with Feynman diagrams regularized using dimensional regularization.
The Aharonov-Casher problem in the presence of a Lorentz-violating background nonminimally coupled to a spinor and a gauge field is examined. Using an approach based on the self-adjoint extension method, an expression for the bound state energies is obtained in terms of the physics of the problem by determining the self-adjoint extension parameter.
We show that in the functional integral formalism the (finite) coefficient of the induced, Lorentz- and CPT-violating Chern-Simons term, arising from the Lorentz- and CPT-violating fermion sector, is undetermined.
We show that the general Lorentz- and CPT-violating extension of quantum electrodynamics is one-loop renormalizable. The one-loop Lorentz-violating beta functions are obtained, and the running of the coefficients for Lorentz and CPT violation is determined. Some implications for theory and experiment are discussed.
This paper shows that the positive-energy and non-renormalization theorems of traditional supersymmetry survive the addition of Lorentz violating interactions. The Lorentz-violating coupling constants in theories using the construction of Berger and Kostelecky must obey certain constraints in order to preserve the positive energy theorem. Seiberg's holomorphic arguments are used to prove that the superpotential remains non-renormalized (perturbatively) in the presence of Lorentz-violating interactions of the Berger-Kostelecky type. We briefly comment on Lorentz-violating theories of the type c…
We identify a fairly general class of field configurations (of spins 0, 1/2 and 1) which preserve Lorentz invariance in effective field theories of Lorentz violation characterized by a constant timelike vector. These fields concomitantly satisfy the equations of motion yielding cubic dispersion relations similar to those found earlier. They appear to have prospective applications in inflationary scenarios.
We probe the influence of Lorentz-violating mechanism, treated exactly, on the radiative quantum corrections to critical exponents for massive $q$-deformed O($N$) $λϕ^{4}$ scalar field theories. We attain that task by employing three distinct and independent field-theoretic renormalization group methods. Firstly we compute the critical exponents up to the finite next-to-leading order for then generalizing the results for any loop level. We show that the $q$-deformed critical exponents are insensible to the Lorentz symmetry breaking mechanism thus agreeing with the universality hypothesis.
We explore the impact of Lorentz violation on the inflationary scenario. More precisely, we study the inflationary scenario in the scalar-vector-tensor theory where the vector is constrained to be unit and time like. It turns out that the Lorentz violating vector affects the dynamics of the chaotic inflationary model and divides the inflationary stage into two parts; the Lorentz violating stage and the standard slow roll stage. We show that the universe is expanding as an exact de Sitter spacetime in the Lorentz violating stage although the inflaton field is rolling down the potential. Much mo…
The two-dimensional aether-superspace is constructed and the superfield techniques are applied to the study of dynamical generation of mass in the Lorentz-violating supersymmetric quantum electrodynamics in two dimensions of spacetime. It is shown that such model presents a dynamical generation of mass to the gauge aether-superfield and its dispersion relation has the structure similar of the CPT-even Lorentz-breaking models.
In this work we study the issue of gauge anomalies in Lorentz-violating QED. To do so, we opt to use the Becchi-Rouet-Stora-Tyutin formalism within the algebraic renormalization approach, reducing our study to a cohomology problem. Since this approach is independent of the renormalization scheme, the results obtained here are expected to be general. We find that the Lorentz-violating QED is free of gauge anomalies to all orders in perturbation theory.
We calculate the induced Lorentz- and CPT-violating Chern-Simons term arising from the Lorentz- and CPT-violating sector of quantum electrodynamics with a $b_μ\barψγ^μγ_5ψ$ term. The result to all orders in $b$ coincides with the previous linear-in-$b$ calulation by Chung and Oh [hep-th/9812132] as well as Jackiw and Kostelecký [Phys. Rev. Lett. {\bf 82}, 3572 (1999)], since all higher order terms vanish.
The role played by a Lorentz-violating term on the outcomes of kink scattering in the $ϕ^6$ model is investigated by using the Fourier spectral method. Impacts of the Lorentz-violating term on the critical velocities, the location of two-bounce windows, and the maximal values of various types of energy densities are analyzed. Some novel features of kink-antikink collisions are discussed. The interactions between three and four kinks are also considered.
We consider one-loop radiative corrections from Lorentz- and CPT- violating extended QED to address the specific problem of finding explicitly an effective action describing amplitude of photon triple splitting. We show that it is not possible to find a nonzero photon triple splitting effective action, at least by using the derivative expansion method (at zero external momenta), up to leading order in the Lorentz- and CPT- violating parameter.
In this paper we study the one- and two-loop contribution to the free energy in QED with the Lorentz symmetry breaking introduced via constant CPT-even Lorentz-breaking parameters at the high temperature limit. We find the impact of the Lorentz-violating term for the free energy and carry out a numerical estimation for the Lorentz-breaking parameter.
The finding of an explicit effective action describing amplitude of photon triple splitting is investigated through Krein space quantization and quantum metric fluctuation. Using the derivative expansion method, the one-loop radiative corrections from Lorentz- and CPT- violating extended Krein QED shows that it is not possible to find a nonzero effective action.
Lorentz-Violating (Regular) Black Holes in Einstein Gravity
Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University（天津大学理学院物理系联合量子研究中心）；The International Joint Institute of Tianjin University, Fuzhou, Tianjin University（天津大学福州国际联合学院）
We calculate a finite momentum-dependent part of the photon polarization operator in a simple model of Lorentz-violating quantum electrodynamics nonperturbatively at all orders of Lorentz-violating parameters. We sum one-particle reducible diagrams into the modified photon propagator, and determine the physical photon dispersion relation as the location of its pole. The photon dispersion relation, as well as its group velocity, acquires the one-loop momentum-dependent radiative correction. We constrain the Lorentz-violating parameters for heavy charged fermions (muon, $τ$-lepton, top-quark) fr…
This paper investigates the Casimir Energy modifications due to the Lorentz-violating CPT-even contribution in an extension of the scalar QED. We have considered the complex scalar field satisfying Dirichlet boundary conditions between two parallel plates separated by a small distance. An appropriate tensor parametrization allowed us to study the Casimir effect in three setups: isotropic, anisotropic parity-odd, and anisotropic parity-even. We have shown that the Lorentz-violating contributions promote increased Casimir energy for both the isotropic and anisotropic parity-odd configurations. H…
Assuming Lorentz symmetry is broken by some fixed vector background, we study the spinor electrodynamics modified by two dimension-five Lorentz-violating interactions between fermions and photons. The effective polarization and magnetization are identified from the modified Maxwell equations, and the theoretical consequences are investigated. We also compute the corrections to the relativistic energy levels of hydrogen atom induced by these Lorentz-violating operators in the absence and presence of uniform external fields in first-order perturbation theory. We find that the hydrogen spectrum i…
In this work, kink-antikink collision in a two-dimensional Lorentz-violating $ϕ^4$ model is considered. It is shown that the Lorentz-violating term in the proposed model does not affect the structure of the linear perturbation spectrum of the standard $ϕ^4$ model, and thus there exists only one vibrational mode. The Lorentz-violating term impacts, however, the frequency and spatial wave function of the vibrational mode. As a consequence, the well-known results on $ϕ^4$ kink-antikink collision will also change. Collisions of kink-antikink pairs with different values of initial velocities and Lo…
We derive the free energy of a Lorentz invariance violating (LIV) O(2) model, for which a non-vanishing commutator among it's momenta is supposed. Then we investigate the possible implications of such a matter field on the time evolution of a flat FRW universe at low and high temperatures.
We consider a cosmological setup with the inflaton field in the presence of a redshift dependent Lorentz-violating time-like background to address the inflationary regime and other phases of the Universe. We also show that the regime of dark energy at large distances (low redshifts) is essentially dominated by the presence of the Lorentz-violating background.
In this work we present a class of traveling solitons in Lorentz-violating systems. In the case of Lorentz violating scenarios, it is usual to construct static solitonic configurations. Here it is shown that it is possible to construct some traveling solitons which, as it should be expected, can not be mapped into a static configuration by means of Lorentz boosts due to its explicit breaking. Furthermore, in the model studied, a complete set of solutions is obtained. The solutions present a critical behavior controlled by the choose of an arbitrary integration constant.
We examine the radiative corrections to an extension of the standard model containing a Lorentz-violating axial vector parameter. At second order in this parameter, the photon self-energy is known to contain terms that violate gauge invariance. Previously, this has been treated as a pathology, but it is also possible to take the gauge noninvariant terms at face value. These terms then make Lorentz-violating contributions to the photon mass, and directly measured limits on the photon mass can be used to set bounds on the Lorentz violation at better than the 10^-22 GeV level.
We give a complete classification of mass dimension five Lorentz-non-invariant interactions composed from the Standard Model fields, using the effective field theory approach. We identify different classes of Lorentz violating operators, some of which are protected against transmutation to lower dimensions even at the loop level. Within each class of operators we determine a typical experimental sensitivity to the size of Lorentz violation.
We investigate the occurrence of ambiguities for Lorentz-violating gravitational Chern-Simons term. It turns out that this term is accompanied by a coefficient depending on an undetermined parameter, due to an arbitrariness in the choice of the conserved current.
I present a topological defect solution that arises in a theory where Lorentz symmetry is spontaneously broken by a rank-two antisymmetric tensor field, and I discuss its observational signatures.
We search for novel Lorentz- and CPT-violating field theories, beyond those contained in the superficially renormalizable standard model extension. We find a new class of scalar field self-interactions which are nonpolynomial in form, involving arbitrarily high powers of the field. Many of these interactions correspond to nontrivial asymptotically free theories. These theories are stable if rotation invariance remains unbroken. These results indicate that certain forms of Lorentz violation, if they exist, may naturally be quite strong.
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…
This paper presents divergent contributions of the radiative corrections for a Lorentz-violating extension of the scalar electrodynamics. We initially discuss some features of the model and extract the Feynman rules. Then we compute the one-loop radiative corrections using Feynman parametrization and dimensional regularization in order to evaluate the integrals. We also discuss Furry's theorem validity and renormalization in the present context.
We have analyzed Maxwell-Chern-Simons-Higgs BPS vortices in a Lorentz-violating CPT-odd context. The Lorentz violation induces profiles with a conical behavior at the origin. For some combination of the coefficients for Lorentz violation there always exists a sufficiently large winding number for which the magnetic field flips its sign.
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…
In this work we make use of proper-time method to evaluate Schwinger effect in the presence of Lorentz-violating background fields. Specifically, we evaluate the one-loop effective Lagrangian in the presence of Lorentz-violating time-like vector background $b_μ$ and pseud-scalar $m_5$ for the pure electric case. The imaginary part of the effective Lagrangian is computed in order to calculate the Schwinger effect. Comments on phenomenology are also performed.
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…
We study the possibility of constructing Lorentz-violating supersymmetric quantum field theories under the assumption that these theories have to be described by lagrangians which are renormalizable by weighted power counting. Our investigation starts from the observation that at high energies Lorentz-violation and the usual supersymmetry algebra are algebraically compatible. Demanding linearity of the supercharges we see that the requirement of renormalizability drastically restricts the set of possible Lorentz-violating supersymmetric theories. In particular, in the case of supersymmetric ga…
The standard forms of supersymmetry and supergravity are inextricably wedded to Lorentz invariance. Here a Lorentz-violating form of supergravity is proposed. The superpartners have exotic properties that are not possible in a theory with exact Lorentz symmetry and microcausality. For example, the bosonic sfermions have spin 1/2 and the fermionic gauginos have spin 1. The theory is based on a phenomenological action that is shown to follow from a simple microscopic and statistical picture.
We consider the role of the velocity in Lorentz-violating fermionic quantum theory, especially emphasizing the nonrelativistic regime. Information about the velocity will be important for the kinematical analysis of scattering and other problems. Working within the minimal standard model extension, we derive new expressions for the velocity. We find that generic momentum and spin eigenstates may not have well-defined velocities. We also demonstrate how several different techniques may be used to shed light on different aspects of the problem. A relativistic operator analysis allows us to study…
In theories with broken Lorentz symmetry, Cerenkov radiation may be possible even in vacuum. We analyze the Cerenkov emissions that are associated with the least constrained Lorentz-violating modifications of the photon sector, calculating the threshold energy, the frequency spectrum, and the shape of the Mach cone. In order to obtain sensible results for the total power emitted, we must make use of information contained within the theory which indicates at what scale new physics must enter.
The fermionic f coefficient in the Lorentz-violating standard model extension presents a puzzle. Thus far, no observable quantity that depends upon f has ever been found. We show that this is because f is actually unnecessary. It has absolutely no effects at leading order and can be completely absorbed into other coefficients of the theory by a redefinition of the field.
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.
S-matrix amplitudes for the electron-electron scattering are calculated in order to verify the quantum equivalence of dual models. We used an extended Quantum Electrodynamics with CPT-even Lorentz-violating kinetic and mass terms, which was used in a process of gauge embedding, known as Noether dualizationn method (NDM), in order to generate its gauge-invariant dual model. The physical equivalence was established at tree-level and the cross section was calculated to second order in the Lorentz-violating parameter.
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.
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…
We propose a new \emph{CPT}-even and Lorentz-violating nonminimal coupling between fermions and Abelian gauge fields involving the CPT-even tensor $(K_{F})_{μναβ}$ of the standard model extension. We thus investigate its effects on the cross section of the electron-positron scattering by analyzing the process $e^{+}+e^{-}\rightarrowμ^{+}+μ^{-}$. Such a study was performed for the parity-odd and parity-even nonbirefringent components of the Lorentz-violating $(K_{F})_{μναβ}$ tensor. Finally, by using experimental data available in the literature, we have imposed upper bounds as tight as $10^{-1…
We demonstrate generation of the two-dimensional Chern-Simons-like Lorentz-breaking action via an appropriate Lorentz-breaking coupling of scalar and spinor fields at zero as well as at the finite temperature and via the noncommutative fields method and study the dispersion relations corresponding to this action.
A Lorentz violating modification of massless QED is proposed, with higher order space derivatives for the photon field. The fermion dynamical mass generation is studied with the Schwinger-Dyson approach, and it is found that the resulting mass is many orders of magnitude smaller than the (Plank-) mass scale introduced by the higher order derivative terms. This is due to a suppressing factor, non-analytic in the fine structure constant and exponentially small. This scenario is an alternative to the Higgs mechanism for the electron mass, which arises here from Lorentz violating effects at high e…
The fundamental issues of microcausality and energy positivity conditions are important to be investigated in the context of spontaneous Lorentz violating theories. We check the microcausality and energy positivity conditions for a free rank-2 antisymmetric tensor field with spontaneous Lorentz violating term and a classically equivalent vector theory from dispersion relations and propagators, and find that the two theories lead to different conditions. While the antisymmetric tensor theory satisfies energy positivity condition and can satisfy microcausality condition for a particular choice o…
We explore the properties of a new Maxwell electrodynamics coupled to a Lorentz-violating background through the presence of higher-derivative terms. Physical implications of this alternative effective theory modified by Lorentz-violating operators of mass dimension-$5$ are considered, such as modified dispersion relations which exhibit the vacuum birefringence phenomenon. Subsequently, we analyze the energy-momentum tensor in the case we reproduce the Gambini-Pullin electrodynamics. We explicitly show that for a background time-like four-vector, $n^μ$, the equations of motion indeed reproduce…
The influence of Lorentz- and CPT-violating terms of the extended Standard Model on a semi-classical two-level system is analyzed. It is shown that the Lorentz-violating background (when coupled with the fermion sector in a vector way) is able to induce modifications on the Rabi oscillation pattern, promoting sensitive modulations on the usual oscillations. As for the term involving the coefficient coupled in an axial vector way, it brings about oscillations both on energy states and on the spin states (implied by the background). It is also seen that such backgrounds are able to yield state o…
Effective quantum field theories that allow for the possibility of Lorentz symmetry violation can sometimes also include redundancies of description in their Lagrangians. Explicit calculations in a Lorentz-violating generalization of Yukawa theory show that when this kind of redundancy exists, different renormalization schemes may lead to different expressions for the renormalization group $β$-functions, even at only one-loop order. However, the renormalization group scaling of physically observable quantities appears not to share this kind of scheme dependence.
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 propose a CPT-even and Lorentz-violating dimension-five nonminimal coupling between fermionic and gauge fields, involving the CPT-even and Lorentz-violating gauge tensor of the Standard-Model Extension. This nonminimal coupling modifies the nonrelativistic regime of Dirac particles, inducing new effects such as an electric-Zeeman-like spectrum splitting and an anomalous-like contribution to the electron magnetic moment. These new effects allow to constrain the magnitude of this nonminimal coupling in 1 part in $10^{16}.$
Inspired in discussions presented lately regarding Lorentz-violating interaction terms in \cite{13,6}, we propose here a slightly different version for the coupling term. We will consider a modified quantum electrodynamics with violation of Lorentz symmetry defined in a $\left( 2+1\right) $-dimensional spacetime. We define the Lagrangian density with a Lorentz-violating interaction, where the the spacetime dimensionality is explicitly taken into account in its definition. The work encompasses an analysis of this model at both zero and finite-temperature, where very interesting features are kno…
We study the dimensional reduction for a $(3+1)$-dimensional Lorentz Violating Lagrangian in the matter and gauge sectors in a Supersymmetric scenario. We thus obtain an effective model for photons induced by the effects of supersymmetry in our framework with Lorentz-symmetry violating. This model is discussed in connection with the attainment of a static potential between charged particles. Our calculation is done within the framework of the gauge-invariant, but path-dependent variable formalism. We thus find that the interaction energy displays a screening part, encoded by Bessel functions, …
