We study phenomena predicted by a renormalizable, CPT invariant extension of the Standard Model that contains higher-dimensional operators and violates Lorentz symmetry explicitly at energies greater than some scale Lambda_{L}. In particular, we consider the Cherenkov radiation in vacuo. In a rather general class of dispersion relations, there exists an energy threshold above which radiation is emitted. The threshold is enhanced in composite particles by a sort of kinematic screening mechanism. We study the energy loss and compare the predictions of our model with known experimental bounds on Lorentz violating parameters and observations of ultrahigh-energy cosmic rays. We argue that the scale of Lorentz violation Lambda_{L} (with preserved CPT invariance) can be smaller than the Planck scale, actually as small as 10^{14}-10^{15} GeV. Our model also predicts the Cherenkov radiation of neutral particles.
We consider a CPT-noninvariant scalar model and a modified version of quantum electrodynamics with an additional photonic Chern-Simons-like term in the action. In both cases, the Lorentz violation traces back to a spacelike background vector. The effects of the modified field equations and dispersion relations on the kinematics and dynamics of decay processes are discussed, first for the simple scalar model and then for modified quantum electrodynamics. The decay widths for electron Cherenkov radiation in modified quantum electrodynamics and for photon triple-splitting in the corresponding low…
We study the Cherenkov effect in the context of the Maxwell-Chern-Simons (MCS) limit of the Standard Model Extension. We present a method to determine the exact radiation rate for a point charge.
The current article reviews results on vacuum Cherenkov radiation obtained for modified fermions. Two classes of processes can occur that have completely distinct characteristics. The first one does not include a spin flip of the radiating fermion, whereas the second one does. A résumé will be given of the decay rates for these processes and their properties.
We show that in the framework of noncommutative classical electrodynamics Cherenkov radiation is permitted in vacuum and we explicitly compute its spectrum at first order in the noncommutative parameter. We discuss the phenomenological impact of the merge of this new analysis with the old results of the substantial modification to the spectrum of the synchrotron radiation obtained in P.Castorina, A.Iorio and D.Zappala, Phys. Rev. D 69 (2004)065008. We propose to consider the pulsars' radiation spectrum - due to its very strong magnetic field - to investigate these Lorentz violating effects in …
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.
Radiative corrections arising from Lorentz violation in the fermion sector induce a nonzero amplitude for vacuum photon splitting. At one loop, the on-shell amplitude acquires both CPT-even and CPT-odd contributions forbidden in conventional electrodynamics.
We study some observational signatures of nonlinearities of the electromagnetic field. First to all we show the vital role played by nonlinearities in triggering a material behavior of the vacuum with $(\varepsilon > 0, μ<0)$, which corresponds to a ferrimagnetic material. Secondly, the permittivity and susceptibility induced by nonlinearities are considered in order to obtain the refractive index via the dispersion relation for logarithmic electrodynamics. Finally, we consider the electromagnetic radiation produced by a moving charged particle interacting with a medium characterized by nonlin…
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.
This work reviews our current understanding of Cherenkov-type processes in vacuum that may occur due to a possible violation of Lorentz invariance. The description of Lorentz violation is based on the Standard Model Extension (SME). To get an overview as general as possible, the most important findings for vacuum Cherenkov radiation in Minkowski spacetime are discussed. After doing so, special emphasis is put on gravitational Cherenkov radiation. For a better understanding, the essential properties of the gravitational SME are recalled in this context. The common grounds and differences of vac…
In the framework of Carrol-Field-Jackiw electrodynamics we calculate the spectral distribution of the Cherenkov radiation (CHR) produced by a charge moving at constant velocity in a chiral medium. We find zero, one or two Cherenkov angles according to the relation between the velocity of the particle and the refraction index of the medium.
The current paper summarizes the content of a talk given on vacuum Cherenkov radiation emitted by Lorentz-violating fermions that are described in the context of the Standard-Model Extension. The decay rate will be obtained for various sets of controlling coefficients that will subsequently be constrained using cosmic-ray data.
We review some of the basic features and predictions of a gauge invariant spontaneous Lorentz symmetry breaking model arising from the nonzero vacuum expectation value of the electromagnetic tensor and leading to a nonlinear electrodynamics. The model is stable in the small Lorentz invariance violation approximation. The speed of light is independent of the frequency and one of the propagating modes is highly anisotropic. The bound (Delta c)/c < 10^{-32} is obtained for such anisotropy measured in perpendicular directions.
The emission of electromagnetic radiation by charges moving uniformly in a Lorentz-violating vacuum is studied. The analysis is performed within the classical Maxwell-Chern-Simons limit of the Standard-Model Extension (SME) and confirms the possibility of a Cherenkov-type effect. In this context, various properties of Cherenkov radiation including the rate, polarization, and propagation features, are discussed, and the back-reaction on the charge is investigated. An interpretation of this effect supplementing the conventional one is given. The emerging physical picture leads to a universal met…
We study radiative corrections to massless quantum electrodynamics modified by two dimension-five LV interactions $\barΨ γ^μ b'^ν F_{μν}Ψ$ and $\barΨγ^μb^ν \tilde{F}_{μν} Ψ$ in the framework of effective field theories. All divergent one-particle-irreducible Feynman diagrams are calculated at one-loop order and several related issues are discussed. It is found that massless quantum electrodynamics modified by the interaction $\barΨ γ^μ b'^ν F_{μν}Ψ$ alone is one-loop renormalizable and the result can be understood on the grounds of symmetry. In this context the one-loop Lorentz-violating beta …
In this work we report new results concerning the question of dynamical mass generation in the Lorentz and PCT violating quantum electrodynamics. A one loop calculation for the vacuum polarization tensor is presented. The electron propagator, "dressed" by a Lorentz breaking extra term in the fermion Lagrangian density, is approximated by its first order: this scheme is shown to break gauge invariance. Then we rather consider a full calculation to second order in the Lorentz breaking parameter: we recover gauge invariance and use the Schwinger-Dyson equation to discuss the full photon propagato…
In this work, we consider the Hořava-Lifshitz scaling to rewrite higher-order derivatives in Lorentz-violating CPT-even electrodynamics. The possibility of the Lorentz invariance violation being originally suppressed by the quantum gravity energy scale $M_{\rm QG}$, may be indeed circumvented in a scenario with anisotropy between space and time above certain intermediate energy scale $Λ_{\rm HL} \ll M_{\rm QG}$. To test the model, we have used observational results of a cosmological time delay between high and low energy photons from gamma ray bursts (GRB090510) event. For specific values of t…
The current work focuses on the process of vacuum Cherenkov radiation for Lorentz-violating fermions that are described by the minimal Standard-Model Extension (SME). To date, most considerations of this important hypothetical process have been restricted to Lorentz-violating photons, as the necessary theoretical tools for the SME fermion sector have not been available. With their development in a very recent paper, we are now in a position to compute the decay rates based on a modified Dirac theory. Two realizations of the Cherenkov process are studied. In the first scenario, the spin project…
Infrared, optical, and ultraviolet spectropolarimetry of cosmological sources is used to constrain the pure electromagnetic sector of a general Lorentz-violating standard-model extension. The coefficients for Lorentz violation are bounded to less than 3x10^{-32}.
Recently proposed Lorentz-PCT noninvariant modifications of electromagnetism are reviewed. Their experimental consequences are described, and it is argued that available data decisively rules out their occurrence in Nature.
The breaking of Lorentz symmetry via a dynamical mechanism, with a tensor field which takes on a non-zero expectation value in vacuum, has been a subject of significant research activity in recent years. In certain models of this type, the perturbations of the "Lorentz-violating field" about this background may be identified with known forces. I present the results of applying this interpretation to the "generalized bumblebee models" found in a prior work. In this model, the perturbations of a Lorentz-violating vector field can be interpreted as a photon field. However, the speed of propagatio…
In a nonperturbative formulation, radiative corrections arising from Lorentz and CPT violation in the fermion sector induce a definite and nonzero Chern-Simons addition to the electromagnetic action. If instead a perturbative formulation is used, an infinite class of theories characterized by the value of the Chern-Simons coefficient emerges at the quantum level.
In this talk presented at the Fourth International Workshop on New Worlds in Astroparticle Physics, I discuss recent constraints on Lorentz violation in electrodynamics. The observed absence of birefringence of light that has propagated over cosmological distances bounds some coefficients for Lorentz violation to 2 x 10^{-32}.
Limits on gravitational Cherenkov radiation by cosmic rays are obtained and used to constrain coefficients for Lorentz violation in the gravity sector associated with operators of even mass dimensions, including orientation-dependent effects. We use existing data from cosmic-ray telescopes to obtain conservative two-sided constraints on 80 distinct Lorentz-violating operators of dimensions four, six, and eight, along with conservative one-sided constraints on three others. Existing limits on the nine minimal operators at dimension four are improved by factors of up to a billion, while 74 of ou…
Vacuum birefringence is a signature of Lorentz-symmetry violation. Here we report on a recent search for birefringence in the cosmic microwave background. Polarization data is used to place constraints on certain forms of Lorentz violation.
The equations of massive electrodynamics are derived and the power spectrum formula for the Cherenkov radiation of massive photons is found. The Cherenkov power spectrum is determined also for the two-charge system. It is argued that the massive Cherenkov effect can be observed in superconductive media, ionosphere plasma, waveguides and in particle laboratories.
An investigation is performed of the Lorentz-violating electrodynamics extracted from the renormalizable sector of the general Lorentz- and CPT-violating standard-model extension. Among the unconventional properties of radiation arising from Lorentz violation is birefringence of the vacuum. Limits on the dispersion of light produced by galactic and extragalactic objects provide bounds of 3 x 10^{-16} on certain coefficients for Lorentz violation in the photon sector. The comparative spectral polarimetry of light from cosmologically distant sources yields stringent constraints of 2 x 10^{-32}. …
The prospects are explored for testing Lorentz- and CPT-violating quantum electrodynamics in experiments with Penning traps. We present the Lagrange density of Lorentz-violating spinor electrodynamics with operators of mass dimensions up to six, and we discuss some of its properties. The theory is used to derive Lorentz- and CPT-violating perturbative shifts of the energy levels of a particle confined to a Penning trap. Observable signals are discussed for trapped electrons, positrons, protons, and antiprotons. Existing experimental measurements on anomaly frequencies are used to extract new o…
The spontaneous Lorentz invariance violation (SLIV) developing in QED type theories with the nonlinear four-vector field constraint $A_μ^{2}=M^{2}$ (where $M$ is a proposed scale of the Lorentz violation) is considered in the case when the internal U(1) charge symmetry is also spontaneously broken. We show that such a SLIV pattern induces the genuine vector Goldstone boson which appears massless when the U(1) symmetry is exact and becomes massive in its broken phase. However, for both of phases an apparent Lorentz violation is completely canceled out in all the observable processes so that the…
We investigate the precisely measured anomalous magnetic moment and Lamb shift as tests for the possible existence of the radiatively induced Lorentz and CPT violation effects in quantum electrodynamics. To this end we calculate the one-loop vacuum polarization tensor and vertex radiative correction in dimensional reduction and on-shell renormalization scheme. We explicitly show how the Lorentz and CPT violation sector affects the anomalous magnetic moment and Lamb shift. Remarkably, we find infrared divergences coming from Lorentz and CPT violating term that do not cancel in physical cross se…
Possible Lorentz-violating effects in the cosmic microwave background are studied. We provide a systematic classification of renormalizable and nonrenormalizable operators for Lorentz violation in electrodynamics and use polarimetric observations to search for the associated violations.
The Standard-Model Extension (SME) provides a theoretical framework for tests of Lorentz invariance. To date, most studies have focused on the minimal SME, which restricts attention to operators of renormalizable dimension. Here, we review recent studies involving the nonrenormalizable photon sector of the SME.
In Lorentz-violating electrodynamics a steady current (and similarly a static charge) generates both static magnetic and electric fields. These induced fields, acting on interfering particles, change the interference pattern. We find that particle interference experiments are sensitive to small Lorentz violating effects, and thus they can be used to improve current bounds on some Lorentz-violating parameters.
Electromagnetic resonant cavities form the basis for a number modern tests of Lorentz invariance. The geometry of most of these experiments implies unsuppressed sensitivities to parity-even Lorentz violations only. Parity-odd violations typically enter through suppressed boost effects, causing a reduction in sensitivity by roughly four orders of magnitude. Here we discuss possible techniques for achieving unsuppressed sensitivities to parity-odd violations by using asymmetric resonators.
Stringent limits on the Myers-Pospelov timelike parameter for photons $ξ<10^{-15}$ coming from astrophysical tests suggest exploring more general preferred backgrounds, such as spacelike and lightlike. We take some steps in this direction. We allow the external four vector $n$ characterizing the Lorentz symmetry breaking to have arbitrary directions in spacetime. We study the consistency for the effective field theories in each privileged frame by demanding causality, stability and analyticity. When specializing to a timelike background we found runaway solutions leading to causality and unita…
It has been argued in hep-ph/0212382 that there may be observable effects from photon triple splitting in an extended version of quantum electrodynamics with Lorentz violation in the fermion sector. The argument is based on an analogy with photon splitting via collinear parametric down-conversion in optically active crystals. In this Comment, we point out that the analogy is misleading and that, at the order considered, the probability of on-shell photon triple splitting is strictly zero.
After imposing the Gauss law constraint as an initial condition upon the Hilbert space of the Nambu model, in all its generic realizations, we recover QED in the corresponding non-linear gauge A_μA^μ=n^{2}M^{2}. Our result is non-perturbative in the parameter M for n^{2}\neq 0 and can be extended to the n^{2}=0 case. This shows that in the Nambu model, spontaneous Lorentz symmetry breaking dynamically generates gauge invariance, provided the Gauss law is imposed as an initial condition. In this way electrodynamics is recovered, with the photon being realized as the Nambu-Goldstone modes of the…
We look for modifications that can be derived from the Maxwell sector of the SME for the interaction between electrical charges and the electromagnetic field. The kind of problem that we are looking into is the one that might be found in a standard textbook on electromagnetism: given a set of electrical charges, in the presence of some non-trivial boundary condition (such as a mirror), find the electromagnetic field and the interaction energy between those charges. To study such kind of problem in the presence of LV coefficients, we calculate the modified propagator for the Maxwell field, and …
The CPT-odd and Lorentz-violating Carroll-Field-Jackiw modification of electrodynamics is discussed and we study its effects on the energy spectrum of hydrogen, as well as in the generation of a momentum-dependent electric dipole moment for charged leptons. We also briefly comment on the possibility of the detection of Lorentz violation in measurements of vacuum birefringence in resonant cavities. The bounds found are based on local laboratory experimental limits and are not competitive with the ones coming from astrophysical considerations.
After summarizing the most interesting results in the calculation of synchrotron radiation in the Myers-Pospelov effective model for Lorentz invariance violating (LIV) electrodynamics, we present a general unified way of describing the radiation regime of LIV electrodynamics which include the following three different models : Gambini-Pullin, Ellis et al. and Myers-Pospelov. Such unification reduces to the standard approach of radiation in a dispersive and absortive (in general) medium with a given index of refraction. The formulation is presented up to second order in the LIV parameter and it…
Synchrotron radiation is analyzed in the classical effective Lorentz invariance violating model of Myers-Pospelov. Within the full far-field approximation we compute the electric and magnetic fields, the angular distribution of the power spectrum and the total emitted power in the m-th harmonic, as well as the polarization. We find the appearance of rather unexpected and large amplifying factors, which go together with the otherwise negligible naive expansion parameter. This opens up the possibility of further exploring Lorentz invariance violations by synchrotron radiation measurements in ast…
Renormalizability of the (minimal) single-fermion QED extension is investigated at all orders of perturbation theory in the framework of algebraic renormalization, a regularization-independent method. Relative to the standard QED, new structures that could lead to gauge anomalies are identified. Nevertheless, even if the anomaly coefficients fail to vanish in the general case, they shall be absent provided we require invariance of the action under C and/or PT transformations. Stability is also verified in this case, hence full renormalizability is attained.
We report the first operation of a rotating odd-parity Lorentz Invariance test in electrodynamics using a microwave Mach-Zehnder interferometer with permeable material in one arm. The experiment sets a direct bound to $ κ_{tr}$ of $-0.3\pm 3\times10^{-7}$. Using new power recycled waveguide interferometer techniques (with the highest spectral resolution ever achieved of $2\times10^{-11} rad/\sqrt{Hz}$) we show an improvement of several orders of magnitude is attainable in the future.
Theory of Supersymmetric Quantum Electrodynamics is extended by interactions with external vector and tensor backgrounds, that are assumed to be generated by some Lorentz-violating (LV) dynamics at an ultraviolet scale perhaps related to the Planck scale. Exact supersymmetry requires that such interactions correspond to LV operators of dimension five or higher, providing a solution to the naturalness problem in the LV sector. We classify all dimension five and six LV operators, analyze their properties at the quantum level and describe observational consequences of LV in this theory. We show t…
The two-photon production by motion of a charged particle in a medium is considered. This process is called Cherenkov-Compton effect because the production of photons is calculated from the Feynman diagram for the Compton effect in a medium. This process is not forbidden in quantum electrodynamics of dielectric media. The cross section of his process in Mandelstam variables is calculated for pair of photons with one moving at the opposite direction to the electron motion and the second one inside Cherenkov cone. The opposite motion is not caused by the collision with a particle of a medium . T…
We report new results of a test of Lorentz invariance based on the comparison of a cryogenic sapphire microwave resonator and a hydrogen maser. The experimental results are shown together with an extensive analysis of systematic effects. Previously, this experiment has set the most stringent constraint on Kennedy-Thorndike type violations of Lorentz invariance. In this work we present new data and interpret our results in the general Lorentz violating extension of the standard model of particle physics (SME). Within the photon sector of the SME, our experiment is sensitive to seven SME paramet…
In an earlier paper [1] (hep-ph/0408006), the bound on the Standard Model Extension photon-sector parameter $\tildeκ_{tr}$ [2] (hep-ph/0205211) set by the heavy-ion storage-ring experiment of Saathoff et al. [3] was incorrectly reported. We show that the correct bound on $\tildeκ_{tr}$ which resulted from this experiment is in fact $2.2\times 10^{-7}$.
