We determine the effect of a CPT-even and Lorentz violating non-minimal coupling on the differential cross sections for some of the most important tree-level processes in QED, namely, Compton and Bhabha scatterings, as well as electron-positron annihilation. Experimental limits constraining the allowed deviation of the differential cross sections relative to pure QED allow us to place upper bounds on the Lorentz violating parameters. A constraint based on the decay rate of para-positronium is also obtained.
We calculate higher-order quantum contributions in different Lorentz-violating parameters to the gauge sector of the extended QED. As a result of this one-loop calculation, some terms which do not produce first-order corrections, contribute with nontrivial gauge-invariant second-order quantum inductions.
We discuss the regularization and renormalization of QED with Lorentz and CPT violation, and argue that the coefficient of the Chern-Simons term is an independent parameter not determined by gauge invariance. We also study these issues in a model with spontaneous breaking of Lorentz and CPT symmetries and find an explicit relation with the ABJ anomaly. This explains the observed convergence of the induced Chern-Simons term.
We investigate the breakdown of Lorentz symmetry in QED by a CPT violating interaction term consisting of the coupling of an axial fermion current with a constant vector field $b$, in the framework of algebraic renormalization -- a regularization-independent method. We show, to all orders in perturbation theory, that a CPT-odd and Lorentz violating Chern-Simons-like term, definitively, is not radiatively induced by the axial coupling of the fermions with the constant vector $b$.
The unitarity in Lorentz invariance violating QED consisting of standard fermions and higher-order photons of the Myers-Pospelov theory is studied. We find ghost states associated to the higher-order character of the theory which could render the $S$ matrix nonunitary. An explicit calculation to check perturbative unitarity in the process of electron-positron scattering is performed and it is found to be possible to preserve unitarity.
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 unitarity of a Lorentz-invariance violating QED model with higher-order Myers and Pospelov photons coupled to standard fermions is studied. As expected, we find ghost states associated to the higher-order terms that may lead to the loss of unitarity. An explicit calculation to check perturbative unitarity in the process of electron-positron scattering is performed and it is found to be possible to be preserved.
In order to treat loops in the Lorentz-violating QED model, we present a derivation of the QED axial anomaly that specifically highlights the infrared origin of the effect. This is done using dimensional regularization while treating $γ_5$ as a spectator. This enables us to revisit aspects in the fermionic sector of Lorentz-violating QED which have analogous structure to the axial anomaly. In particular, it is shown that both the Chern-Simons and photon mass operators are not induced in the one loop effective action. At lowest order in the Lorentz-violating parameter, we can define a non-relat…
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…
We study a QED extension that is unitary, CPT invariant and super-renormalizable, but violates Lorentz symmetry at high energies, and contains higher-dimension operators (LVQED). Divergent diagrams are only one- and two-loop. We compute the one-loop renormalizations at high and low energies and analyse the relation between them. It emerges that the power-like divergences of the low-energy theory are multiplied by arbitrary constants, inherited by the high-energy theory, and therefore can be set to zero at no cost, bypassing the hierarchy problem.
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…
We reconsider an alternative theory of the QED with the photon as a massless vector Nambu-Goldstone boson and show that the underlying spontaneous Lorentz violation caused by the vector field vacuum expectation value, while being superficial in gauge invariant theory, becomes physically significant in the QED with a tiny gauge non-invariance. This leads, through special dispersion relations appearing for charged fermions, to a new class of phenomena which could be of distinctive observational interest in particle physics and astrophysics. They include a significant change in the GZK cutoff for…
It is by now clear that infrared sector of QED has an intriguingly complex structure. Based on earlier pioneering works on this subject, two of us recently proposed a simple modification of QED by constructing a generalization of the $U(1)$ charge group of QED to the "Sky" group incorporating the known spontaneous Lorentz violation due to infrared photons, but still compatible in particular with locality. There it was shown that the "Sky" group is generated by the algebra of angle dependent charges and a study of its superselection sectors has revealed a manifest description of spontaneous bre…
We consider the four-dimensional quantum electrodynamics extended with Myers-Pospelov Lorentz-violating dimension-5 operators to investigate 4D-2D projection. In projecting out the 4D theory down to a 2D theory we get analogs of these operators. Namely, we obtain a new two-dimensional theory with corresponding scalar and fermionic 2D Myers-Pospelov Lorentz-violating dimension-3 operators. New defect structures can also be found from this new projected out 2D scalar sector. Furthermore, we also show that this 2D scalar sector can be also radiatively induced through the new 2D fermionic sector.
We show that the correctly evaluated effective Lagrangian should include short-distance interaction terms which have been avoided under the protection of usual regularization and must be properly identified and reinstated if regularization is to be removed. They have special physical and mathematical significance as well as restoring gauge invariance and suppressing divergence in the effective Lagrangian. The rich structure of the short-distance interaction terms can open up challenging opportunities where the conventional regularization with rigid structure is unavailable and inappropriate. I…
A theoretical framework extending QED in the context of the standard model is used to analyze a variety of Lorentz and CPT tests in atomic systems. Experimental signatures of possible Lorentz and CPT violation in these systems are investigated, and bounds are discussed.
It has been shown that QED in (1+4)-dimensional space-time, with the fifth dimension compactified on a circle, leads to CP violation (CPV). Depending on fermionic boundary conditions, CPV may be either explicit (through the Scherk--Schwarz mechanism), or spontaneous (via the Hosotani mechanism). The fifth component of the gauge field acquires (at the one-loop level) a non-zero vacuum expectation value. In the presence of two fermionic fields, this leads to spontaneous CPV in the case of CP-symmetric boundary conditions. Phenomenological consequences are illustrated by a calculation of the elec…
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.
A status report is given of some recent theoretical and experimental investigations looking for signals of Lorentz violation in QED. Experiments with light, charged particles, and atoms have exceptional sensitivity to small shifts in energy caused by Lorentz violation, including effects that could originate from new physics at the Planck scale.
The general features of renormalization and the renormalization group in QED and in general quantum field theories in curved spacetime with additional Lorentz- and CPT-violating background fields are reviewed.
We rediscuss the controversy on a possible Chern-Simons like term generated through radiative corrections in QED with a CPT violating term. We analyse some consequences of the division of the Lagrangian density between "free part" and "interaction part". We also emphasize the fact that any absence of an {\sl a priori} divergence should be explained by some symmetry or some non-renormalisation theorem and show that the so-called "unambiguous result" based upon "maximal SO(3) residual symmetry " does not offer a solution.
An analysis of spinor redefinitions in the context of the Lorentz-violating QED extension is performed. Certain parameters that apparently violate Lorentz invariance are found to be physically irrelevant as they can be removed from the lagrangian using an appropriate redefinition of the spinor field components. It is shown that conserved currents may be defined using a modified action of the complex extension of the Lorentz group on the redefined spinors. This implies a natural correspondence between the apparently Lorentz-violating theory and conventional QED. Redefinitions involving derivati…
We revisit the previously unsolved problems of ensuring Lorentz invariance and non-perturbative unitarity in Lee-Wick theories. We base our discussion on an ultraviolet completion of QED by Lee-Wick ghost fields, which is argued to be asymptotically safe. We argue that as long as the state space is based upon a suitable choice of distributions of a type invented by Gel'fand and Shilov, the Lee-Wick ghosts can be eliminated while preserving Lorentz invariance to produce a unitary theory. The method for eliminating ghosts is in principle non-perturbatively well-defined, in contrast with some pre…
This talk summarizes some theoretical features and experimental implications of a general Lorentz-violating extension of the minimal SU(3) x SU(2) x U(1) standard model that allows for both CPT-even and CPT-odd effects. The theory would arise as the low-energy limit of a fundamental theory that is Lorentz and CPT covariant but in which spontaneous Lorentz breaking occurs. The use of neutral-meson oscillations and various QED systems to bound the apparent CPT and Lorentz violations is described.
The variational equation for the mean square displacement of the electron in the polaron worldline approach to quenched QED can be cast into a form which closely resembles the classical Abraham-Lorentz equation but without the conceptual and practical diseases of the latter. The connection with delay equations describing field retardation effects is also established. As applications we solve this integro-differential equation numerically for various values of the coupling constant and cut-off and re-derive the variational approximation to the anomalous mass dimension of the electron found rece…
The strongest bounds on some forms of Lorentz and CPT violation come from astrophysical data, and placing such bounds may require understanding and modeling distant sources of radiation. However, it is also desirable to have bounds that do not rely on these kinds of detailed models. Bounds that do not rely on any modeling of astrophysical objects may be derived both from laboratory experiments and certain kinds of astrophysical observations. The strongest such bounds on isotropic modifications of electron, positron, and photon dispersion relations of the form E^2 = p^2 + m^ 2 + epsilon p^3 com…
We consider Lorentz-violating operators induced at the loop level in softly-broken supersymmetric noncommutative QED. Dangerous operators forbidden in the supersymmetric limit are generated via finite corrections, with the scale of supersymmetry breaking serving as a gauge-invariant regulator. We compare the most dangerous loop effects to those obtained in noncommutative theories truncated by a momentum-space cutoff, and find significantly improved bounds.
In this paper we evaluate the induced Lorentz and CPT violating Chern-Simons term in the QED action at finite temperature. We do this using the method of derivative expansion of fermion determinants. Also, we use the imaginary-time formalism to calculate the temperature dependence of the Chern-Simons term
We analyse the recent controversy on a possible Chern-Simons like term generated through radiative corrections in QED with a CPT violating term : we prove that, if the theory is correctly defined through Ward identities and normalisation conditions, no Chern-Simons term appears, without any ambiguity. This is related to the fact that such a term is a kind of minor modification of the gauge fixing term, and then no renormalised. The past year literature on that subject is discussed, and we insist on the fact that any absence of an {\sl a priori} divergence should be explained by some symmetry o…
Comparing electronic Hydrogen with muonic Hydrogen shows that the discrepancy in measurement of the Lamb shift in the both systems are relatively of order of $(\frac{m_μ}{m_e})^{4-5}$. We explore the spectrum of Hydrogen atom in noncommutative $QED$ to compare the noncommutative effects on the both bound states. We show that in the Lorentz violating noncommutative QED the ratio of NC-corrections is $(\frac{m_μ}{m_e})^3$ while in the Lorentz conserving NCQED is $(\frac{m_μ}{m_e})^5$. An uncertainty about $1 \,Hz\ll 3\,kHz$ in the Lamb shift of Hydrogen atom leads to an NC correction about $10 \…
We show that QED in the Coulomb gauge can be considered as a low energy linear approximation of a non-linear $σ$-type model where the photon emerges as a vector Goldstone boson related to the spontaneous breakdown of Lorentz symmetry down to its spatial rotation subgroup at some high scale $M$. Starting with a general massive vector field theory one naturally arrives at this model if the pure spin-1 value for the vector field $A_μ(x)$ provided by the Lorentz condition $\partial_μA_μ(x)=0$ is required. The model coincides with conventional QED in the Coulomb gauge in the limit of M going to inf…
We obtain the induced Lorentz- and CPT-violating term in QED at finite temperature using imaginary-time formalism and dimensional regularization. Its form resembles a Chern-Simons-like structure, but, unexpectedly, it does not depend on the temporal component of the fixed $b_μ$ constant vector that is coupled to the axial current. Nevertheless Ward identities are respected and its coefficient vanishes at T=0, consistently with previous computations with the same regularization procedure, and it is a non-trivial function of temperature. We argue that at finite $T$ a Chern-Simons-like Lorentz- a…
We present a class of interacting nonlocal quantum field theories, in which the CPT invariance is violated while the Lorentz invariance is present. This result rules out a previous claim in the literature that the CPT violation implies the violation of Lorentz invariance. Furthermore, there exists the reciprocal of this theorem, namely that the violation of Lorentz invariance does not lead to the CPT violation, provided that the residual symmetry of Lorentz invariance admits the proper representation theory for the particles. The latter occurs in the case of quantum field theories on a noncomm…
The general charge-conserving effective scalar field theory incorporating violations of Lorentz symmetry is presented. The dispersion relation is used to infer the effects of spin-independent Lorentz violation on point-particle motion. A large class of associated Finsler spaces is derived, and the properties of these spaces is explored.
The objection [arXiv:1103.0168] to my theorem [arXiv:hep-ph/0201258] that violation of $CPT$ symmetry implies violation of Lorentz covariance is based on a nonlocal model in which time-ordered products are not well defined. I used covariance of time-ordered products as the condition for Lorentz covariance; therefore the proposed objection is not relevant to my result.
We set constraints on O(E/M) Lorentz Violation in QED in an effective field theory framework. A major consequence of such assumptions is the modification of the dispersion relations for electrons/positrons and photons, which in turn can affect the electromagnetic output of astrophysical objects. We compare the information provided by multiwavelength observations with a full and self-consistent computation of the broad-band spectrum of the Crab Nebula. We cast constraints of order 10^{-5} at 95% confidence level on the lepton Lorentz Violation parameters.
I present a unified formulation of anomalous contributions in quantum field theories by calculating directly the effective action using the background field and covariant-derivative expansion technique. I use this method to determine uniquely the induced Chern-Simons term from the a Lorentz and CPT violating term in fermion QED Lagrangian. The outstanding ambiguity is resolved by properly taken into account the noncommutivity of $A$ and $\partial$. The resulting vacuum polarization tensor acquires a non-Feynman diagram anomalous contribution which accounts for the discrepancy between the prese…
In Lorentz- and CPT-violating effective field theories involving scalar and spinor fields, there exist forms of Lorentz violation that modify only the scalar-spinor Yukawa interaction vertices. These affect low-energy fermion and antifermion scattering processes through modifications to the nonrelativistic Yukawa potentials. The modified potentials involve novel combinations of momentum, spin, and Lorentz-violating background tensors.
Supersymmetric field theories can be constructed that violate Lorentz and CPT symmetry. We illustrate this with some simple examples related to the original Wess-Zumino model.
We report that a general principle of physical independence of mathematical background manifolds brings a replacement of common derivative operators by co-derivative ones. Then we obtain a new Lagrangian for the ordinary minimal standard model with supplementary terms containing the Lorentz invariance violation information measured by a new matrix, denoted as the Lorentz invariance violation matrix. We thus provide a new fundamental theory to study Lorentz invariance violation effects consistently and systematically.
Standard model with intrinsic Lorentz and CPT violations is proposed in a Finsler geometric framework. We present explicitly Lorentz and CPT--breaking Lagrangians of the matter fields and the gauge fields in locally Minkowski spacetime. The Lorentz invariance violation is found to be originated from the spacetime background deviating from the Minkowski one. Similarly, the CPT violation is determined by the behaviors of the locally Minkowski metric under the parity and time reversal operations. To help understanding phenomenologies, we compare the Finslerian model with the standard--model exten…
Recently a version of Lorentz-conserving noncommutative field theory (NCFT) has been suggested. The underlying Lie algebra of the theory is the same as that of Doplicher, Fredenhagen, and Roberts. In Lorentz-conserving NCFT the matrix parameter {theta}^{mu nu} which characterizes the canonical NCFT's is promoted to an operator {theta hat}^{mu nu} that transforms as a Lorentz tensor. In this paper, we calculate phenomenological consequences of the QED version of this theory by looking at various collider processes. In particular we calculate modifications to Moller scattering, Bhabha scattering…
We show for the first time that the induced parity--even Lorentz invariance violation can be unambiguously calculated in the physically justified and minimally broken dimensional regularization scheme, suitably tailored for a spontaneous Lorentz symmetry breaking in a field theory model. The quantization of the Lorentz invariance violating quantum electrodynamics is critically examined and shown to be consistent either for a light--like cosmic anisotropy axial--vector or for a time--like one, when in the presence of a bare photon mass.
This paper investigates how the nonzero temperature affects the differential cross-section for mesons scattering in a Lorentz-violating extension of the scalar electrodynamics. We initially discuss some features of the model and extract the zero temperature Feynman rules. Temperature effects are introduced using the Thermo Field Dynamics (TFD) formalism. It is shown that the corrections induced on the meson scattering are very large in the high-temperature regime. Furthermore, our results also suggest that temperature effects may contribute to new constraints on the Lorentz-violating parameter…
We entertain the idea that a suitable background of cold (very low momentum) pseudoscalar particles or condensate, may trigger a background that effectively generates Lorentz-invariance violation. This aether-like background induces a Chern-Simons modification of QED. Physics is different in different frames and, in the rest frame of the pseudoscalar background, high momentum photons can decay into pairs. The threshold for such decay depends quadratically on the rest mass of the particles. This mechanism could explain in a natural way why antiprotons are absent in recent cosmic ray measurement…
We discuss the derivation of the trace anomaly using a non-local effective action at one loop. This provides a simple and instructive form and emphasizes infrared physics. We then use this example to explore several of the properties of non-local actions, including displaying the action for the full non-local energy-momentum tensor. As an application, we show that the long-distance corrections at one loop lead to quantum violations of some classical consequences of the equivalence principle, for example producing a frequency dependence of the gravitational bending of light.
By using path integral formulation of QCD and QED we prove that the factorization theorem is valid for light-like Wilson line but is not valid for non-light-like Wilson line. This conclusion is shown to be consistent with Ward identity and Grammer-Yennie approximation. Hence we find that the factorization theorem is violated in all the previous studies which used the non-light-like Wilson line in the definition of the (transverse momentum dependent) parton distribution function and fragmentation function at high energy colliders.
It was recently suggested that possible small volations of Lorentz invariance could explain the existence of UHECR beyond the GZK cutoff and the observations of multi-TeV gamma-rays from Mkn 501. Our analysis of Lorentz-violating kinematics shows that in addition to the modified threshold conditions solving cosmic ray puzzles we should expect a strong suppression of electromagnetic processes like bremsstrahlung and pair creation. This leads to drastic effects in electron-photon cascade development in the atmosphere and in detectors.
An interacting theory that violates CPT invariance necessarily violates Lorentz invariance. On the other hand, CPT invariance is not sufficient for out-of-cone Lorentz invariance. Theories that violate CPT by having different particle and antiparticle masses must be nonlocal.
Recently, a state of the art experiment shows evidence for Lorentz violation in the gravitational sector. To explain this experiment, we investigate a spontaneous Lorentz violation scenario with a generalized scalar field. We find that when the scalar field is nonminimally coupled to gravity, the Lorentz violation induces a deformation in the Newtonian potential along the direction of Lorentz violation.
The possibility of a small modification of spinor Quantum Electro-Dynamics is reconsidered, in which Lorentz and CPT non-covariant kinetic terms for photons and fermions are present. The corresponding free field theory is carefully discussed. The finite one-loop parity-odd induced effective action is unambiguously calculated using the physical cutoff method, which manifestly encodes the maximal residual symmetry group allowed by the presence of the Lorentz and CPT breaking axial-vector. This very same induced effective action, which is different from those ones so far quoted in the Literature,…
We consider the possibility that Lorentz violation can generate differences between the limiting velocities of light and charged matter. Such effects would lead to efficient vacuum Cherenkov radiation or rapid photon decay. The absence of such effects for 104.5 GeV electrons at the Large Electron Positron collider and for 300 GeV photons at the Tevatron therefore constrains this type of Lorentz breakdown. Within the context of the standard-model extension, these ideas imply an experimental bound at the level of -5.8 x 10^{-12} <= \tildeκ_{tr}-(4/3)c_e^{00} <= 1.2 x 10^{-11} tightening existing…
Any possible Lorentz violation in the hadron sector must be tied to Lorentz violation at the underlying quark level. The relationships between the theories at these two levels are studied using chiral perturbation theory. Starting from a two-flavor quark theory that includes dimension-four Lorentz-violation operators, the effective Lagrangians are derived for both pions and nucleons, with novel terms appearing in both sectors. Since the Lorentz violation coefficients for nucleons and pions are all related to a single set of underlying quark coefficients, it is possible to place approximate bou…
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}.
