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This chapter of the proceedings for the Ninth Meeting on CPT and Lorentz Symmetry is dedicated to the Hamiltonian formulation of the minimal gravitational Standard-Model Extension. Some theoretical questions associated with the latter shall be reviewed. First, we recall the properties of the Hamiltonian, which was computed elsewhere, and discuss how it is linked to the modified Einstein equations. Second, we describe how the covariant and Hamiltonian formulations are shown to be consistent with each other., Comment: Presented at the Ninth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, May 17-26, 2022; 4 pages

The current paper is a technical work that is focused on Lorentz violation for Dirac fermions as well as neutrinos, described within the nonminimal Standard-Model Extension. We intend to derive two theoretical results. The first is the full propagator of the single-fermion Dirac theory modified by Lorentz violation. The second is the dispersion equation for a theory of $N$ neutrino flavors that enables the description of both Dirac and Majorana neutrinos. As the matrix structure of the neutrino field operator is very involved for generic $N$, we will use sophisticated methods of linear algebra to achieve our objectives. Our main finding is that the neutrino dispersion equation has the same structure in terms of Lorentz-violating operators as that of a modified single-fermion Dirac theory. The results will be valuable for phenomenological studies of Lorentz-violating Dirac fermions and neutrinos., Comment: 17 pages

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 r\'{e}sum\'{e} will be given of the decay rates for these processes and their properties., Comment: 4 pages, 2 figures; Presented at the Eighth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, May 12-16, 2019

The current paper is dedicated to determining perturbative expansions for Lagrangians describing classical, relativistic, pointlike particles subject to Lorentz violation parameterized by the nonminimal Standard-Model Extension (SME). An iterative technique recently developed and applied to a Lorentz-violating scalar field theory is now adopted to treat the spin-degenerate SME fermion sector. Lagrangians are obtained at third order in Lorentz violation for the operators $\hat{a}_{\mu}$, $\hat{c}_{\mu}$, $\hat{e}$, $\hat{f}$, and $\hat{m}$ for arbitrary mass dimension. The results demonstrate the impact of nonzero spin on classical particle propagation. They will be useful for phenomenological studies of modified gravity and could provide useful insights into explicit Lorentz violation in curved spacetimes., Comment: 9 pages, prepared for submission to Phys. Lett. B

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., Comment: 5 pages, 2 figures; proceedings for "International workshop on CPT and Lorentz Symmetry in Field Theory" that took place in Faro, Portugal on July 6-7, 2017

In this paper, we derive the general leading-order classical Lagrangian covering all fermion operators of the nonminimal Standard-Model Extension (SME). Such a Lagrangian is considered to be the point-particle analog of the effective field theory description of Lorentz violation that is provided by the SME. First of all, a suitable Ansatz is made for the Lagrangian of the spin-degenerate operators $\hat{a}$, $\hat{c}$, $\hat{e}$, and $\hat{f}$ at leading order in Lorentz violation. The latter is shown to satisfy the set of five nonlinear equations that govern the map from the field theory to the classical description. After doing so, the second step is to propose results for the spin-nondegenerate operators $\hat{b}$, $\hat{d}$, $\hat{H}$, and $\hat{g}$. Although these are more involved than the Lagrangians for the spin-degenerate ones, an analytical proof of their validity is viable, nevertheless. The final step is to combine both findings to produce a generic Lagrangian for the complete set of Lorentz-violating operators that is consistent with the known minimal and nonminimal Lagrangians found in the literature so far. The outcome reveals the leading-order structure of the classical SME analog. It can be of use for both phenomenological studies of classical bodies in gravitational fields and conceptual work on explicit Lorentz violation in gravity. Furthermore, there may be a possible connection to Finsler geometry., Comment: 23 pages

The Standard-Model Extension (SME) parameterizes all possible Lorentz-violating contributions to the Standard Model and General Relativity. It can be considered as an effective framework to describe possible quantum-gravity effects for energies much below the Planck energy. In the current paper, the spin-nondegenerate operators of the SME fermion sector are the focus. The propagators, energies, and solutions to the modified Dirac equation are obtained for several families of coefficients including nonminimal ones. The particle energies and spinors are computed at first order in Lorentz violation and, with the optical theorem, they are shown to be consistent with the propagators. The optical theorem is then also used to derive the matrices formed from a spinor and its Dirac conjugate at all orders in Lorentz violation. The results are the first explicit ones derived for the spin-nondegenerate operators. They will prove helpful for future phenomenological calculations in the SME that rely on the footing of quantum field theory., Comment: 38 pages, 1 figure

This article gives a brief summary on recently obtained classical lagrangians for the nonminimal fermion sector of the Standard-Model Extension (SME). Such lagrangians are adequate descriptions of classical particles that are subject to a Lorentz-violating background field based on the SME. Explicitly, lagrangians were obtained for the leading nonminimal contributions of the m, a, c, e, and f coefficients. These results were then used to interpret classical, kinematic tests of Special Relativity in the framework of the nonminimal SME. This led to new constraints on certain nonminimal controlling coefficients. Although the experiments were very sophisticated in the era when they were carried out, their sensitivities for detecting Lorentz violation were still far away from the Planck scale. Obtaining the novel constraints can be considered as a proof-of-principle demonstrating the applicability of the classical lagrangians computed., Comment: Presented at the Seventh Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 20-24, 2016

The recent direct detection of gravitational waves reported by Advanced LIGO has inspired the current article. In this context, a particular Lorentz-violating framework for classical, massive particles is the focus. The latter is characterized by a preferred direction in spacetime comprised of CPT-odd components with mass dimension 1. Curvature effects in spacetime, which are caused by a propagating gravitational wave, are assumed to deform the otherwise constant background field. In accordance with spontaneous Lorentz violation, a particular choice for the vector field is taken, which was proposed elsewhere. The geodesic equations for a particle that is subject to this type of Lorentz violation are obtained. Subsequently, their numerical solutions are computed and discussed. The particular model considered leads to changes in the particle trajectory whose impact on interferometric gravitational-wave experiments such as LIGO will be studied., Comment: 25 pages, 3 figures, considerably modified manuscript after acceptance by journal

This article is devoted to finding classical point-particle equivalents for the fermion sector of the nonminimal Standard-Model Extension (SME). For a series of nonminimal operators, such Lagrangians are derived at first order in Lorentz violation using the algebraic concept of Gr\"obner bases. Subsequently, the Lagrangians serve as a basis for reanalyzing the results of certain kinematic tests of Special Relativity that were carried out in the last century. Thereby, a number of new constraints on coefficients of the nonminimal SME is obtained. In the last part of the paper we point out connections to Finsler geometry., Comment: 35 pages

The current article shall contribute to understanding the classical analogue of the minimal photon sector in the Lorentz-violating Standard-Model Extension (SME). It is supposed to complement all studies performed on classical point-particle equivalents of SME fermions. The classical analogue of a photon is not a massive particle being described by a usual equation of motion, but a geometric ray underlying the eikonal equation. The first part of the paper will set up the necessary tools to understand this correspondence for interesting cases of the minimal SME photon sector. In conventional optics the eikonal equation follows from an action principle, which is demonstrated to work in most (but not all) Lorentz-violating cases as well. The integrands of the action functional correspond to Finsler structures, which establishes the connection to Finsler geometry. The second part of the article treats Lorentz-violating light rays in a weak gravitational background by implementing the principle of minimal coupling. Thereby it is shown how Lorentz violation in the photon sector can be constrained by measurements of light bending at massive bodies such as the Sun. The phenomenological studies are based on the currently running ESA mission GAIA and the planned NASA/ESA mission LATOR. The final part of the paper discusses certain aspects of explicit Lorentz violation in gravity based on the setting of Finsler geometry., Comment: 63 pages, 4 figures

In this article the classical, relativistic Lagrangian based on the isotropic fermion sector of the Lorentz-violating (minimal) Standard-Model Extension is considered. The motion of the associated classical particle in an external electromagnetic field is studied and the evolution of its spin, which is introduced by hand, is investigated. It is shown that the particle travels along trajectories that are scaled versions of the standard ones. Furthermore there is no spin precession due to Lorentz violation, but the rate is modified at which the longitudinal and transverse spin components transform into each other. This demonstrates that it is practical to consider classical physics within such an isotropic Lorentz-violating framework and it opens the pathway to study a curved background in that context., Comment: 20 pages

The current article deals with analytical bunch compression studies for FLUTE whose results are compared to simulations. FLUTE is a linac-based electron accelerator with a design energy of approximately 40 MeV currently being constructed at the Karlsruhe Institute of Technology. One of the goals of FLUTE is to generate electron bunches with their length lying in the femtosecond regime. In the first phase this will be accomplished using a magnetic bunch compressor. This compressor forms the subject of the studies presented. The paper is divided into three parts. The first part deals with pure geometric investigations of the bunch compressor where space charge effects and the back reaction of bunches with coherent synchrotron radiation (CSR) are neglected. The second part is dedicated to the treatment of space charge effects and the third part gives some analytical results on the emission of CSR. The upshot is that the results of the first and the third part agree quite well with what is obtained from simulations. However, the space charge forces in the analytical model of the second part have the trend to be overestimated for large bunch charges. With this paper we intend to form the basis for future analytical studies of the FLUTE bunch compressor and of bunch compression, in general., Comment: 54 pages, 22 captioned figures

In the current paper the Lagrangian of a classical, relativistic point particle is obtained whose conjugate momentum satisfies the dispersion relation of a quantum wave packet that is subject to Lorentz violation based on a particular coefficient of the nonminimal Standard-Model Extension (SME). The properties of this Lagrangian are analyzed and two corresponding Finsler structures are obtained. One structure describes a scaled Euclidean geometry, whereas the other is neither a Riemann nor a Randers or Kropina structure. The results of the article provide some initial understanding of classical Lagrangians of the nonminimal SME fermion sector., Comment: 26 pages, 5 figures

In the current paper the properties of a quantum field theory based on certain sets of Lorentz-violating coefficients in the nonminimal fermion sector of the Standard-Model Extension are analyzed. In particular, three families of coefficients are considered, where two of them are CPT-even and the third is CPT-odd. As a first step the modified fermion dispersion relations are obtained. Then the positive- and negative-energy solutions of the modified Dirac equation and the fermion propagator are derived. These are used to demonstrate the validity of the optical theorem at tree-level, which provides a cross-check for the results obtained. Furthermore unitarity is examined and seems to be valid for the first set of CPT-even coefficients. However for the remaining sets certain issues with unitarity are found. The article demonstrates that the adapted quantum field theoretical methods at tree-level work for the nonminimal, Lorentz-violating framework considered. Besides, the quantum field theory based on the first family of CPT-even coefficients is most likely well-behaved at lowest order perturbation theory. The results are important for future phenomenological investigations carried out in the context of field theory, e.g., the computation of decay rates and cross sections at tree-level., Comment: 35 pages, 3 figures; version 2.0: added results on reflexion positivity (unitarity), accepted for publication by Phys. Rev. D

In the context of the nonminimal Standard-Model Extension a special subset of the CPT-even higher-dimensional operators in the photon sector is discussed from a quantum-field theoretical point of view. The modified dispersion laws, photon polarization vectors plus the gauge field propagator are obtained and their properties are analyzed. It is demonstrated that for certain sectors of the modified theory a puzzle arises for the optical theorem at tree-level. This is followed by a discussion of how it can be interpreted and resolved at first order Lorentz violation. Furthermore the commutator of two gauge fields that are evaluated at different spacetime points is obtained and discussed. The structure of the theory is shown to resemble the structure of the modification based on the corresponding dimension-4 operator. However some properties are altered due to the nonrenormalizable nature of the theory considered. The results provide more insight into the characteristics of Lorentz-violating quantum field theories that rest upon contributions of nonrenormalizable dimension., Comment: 25 pages, 2 figures

In the current paper the properties of a birefringent Lorentz-violating extension of quantum electrodynamics is considered. The theory results from coupling modified Maxwell theory, which is a CPT-even Lorentz-violating extension of the photon sector, to a Dirac theory of standard spin-1/2 particles. It is then restricted to a special birefringent case with one nonzero Lorentz-violating coefficient. The modified dispersion laws of electromagnetic waves are obtained plus their phase and group velocities are considered. After deriving the photon propagator and the polarization vectors for a special momentum configuration we prove both unitarity at tree-level and microcausality for the quantum field theory based on this Lorentz-violating modification. These analytical proofs are done for a spatial momentum with two vanishing components and the proof of unitarity is supported by numerical investigations in case all components are nonvanishing. The upshot is that the theory is well-behaved within the framework of our assumptions where there is a possible issue for negative Lorentz-violating coefficients. The paper shall provide a basis for the future analysis of alternative birefringent quantum field theories., Comment: 32 pages, 4 figures; in version 3.0: added generalized results on optical theorem

This article reviews the methods used to obtain a two-sided bound on isotropic modified Maxwell theory from experimental data of ultra high-energy cosmic rays in 2008. The bound is updated with results from the HEGRA experiment., Comment: 4 pages, presented at the Sixth Meeting on CPT and Lorentz symmetry; June 17 - 21, 2013; Bloomington, Indiana (USA)

A model in which pointlike defects are randomly embedded in Minkowski spacetime is considered. The distribution of spacetime defects is constructed to be Lorentz-invariant. It does not introduce a preferred reference frame, because it is based on a sprinkling process. A field-theoretic action for the photon and a fermion is set up, in which the photon is assumed not to couple to the defects directly, but via a scalar field. We are interested in signs for Lorentz violation caused by the spacetime defects, which are expected to reveal themselves in the photon sector. A modification of the photon dispersion relation may result as a quantum effect and we compute it at leading order perturbation theory. The outcome of the calculation is that the photon dispersion law remains conventional, if the defect distribution is dense, homogeneous, and isotropic. This result sheds some new light on Lorentz violation in the framework of a small-scale structure of spacetime. It shows that Lorentz invariance can be preserved even in the presence of a spacetime structure that is supposed to emerge at the Planck scale. This conclusion has already been drawn on general grounds in other publications, where the current paper delivers a demonstration by a direct computation in a simple model., Comment: 40 pages, 9 figures

In a previous article [arXiv:1011.4258], we established the consistency of isotropic modified Maxwell theory for a finite range of the Lorentz-violating parameter \tilde{kappa}_{tr}, which includes both positive and negative values of \tilde{kappa}_{tr}. As an aside, we mentioned the existence of a physical model which, for low-energy photons, gives rise to isotropic modified Maxwell theory with a positive parameter \tilde{kappa}_{tr} (corresponding to a "slow" photon). Here, we present a related model which gives rise to isotropic modified Maxwell theory with a negative parameter \tilde{kappa}_{tr} (corresponding to a "fast" photon). Both models have an identical particle content, photon and Dirac particles, but differ in the type of spacetime manifold considered., Comment: 6 pages, v4: published version

We studied the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) like state establishing due to the proximity effect in superconducting Nb/Cu41Ni59 bilayers. Using a special wedge-type deposition technique, series of 20-35 samples could be fabricated by magnetron sputtering during one run. The layer thickness of only a few nanometers, the composition of the alloy, and the quality of interfaces were controlled by Rutherford backscattering spectrometry, high resolution transmission electron microscopy, and Auger spectroscopy. The magnetic properties of the ferromagnetic alloy layer were characterized with superconducting quantum interference device (SQUID) magnetometry. These studies yield precise information about the thickness, and demonstrate the homogeneity of the alloy composition and magnetic properties along the sample series. The dependencies of the critical temperature on the Nb and Cu41Ni59 layer thickness, Tc(dS) and Tc(dF), were investigated for constant thickness dF of the magnetic alloy layer and dS of the superconducting layer, respectively. All types of non-monotonic behaviors of Tc versus dF predicted by the theory could be realized experimentally: from reentrant superconducting behavior with a broad extinction region to a slight suppression of superconductivity with a shallow minimum. Even a double extinction of superconductivity was observed, giving evidence for the multiple reentrant behavior predicted by theory. All critical temperature curves were fitted with suitable sets of parameters. Then, Tc(dF) diagrams of a hypothetical F/S/F spin-switch core structure were calculated using these parameters. Finally, superconducting spin-switch fabrication issues are discussed in detail in view of the achieved results., Comment: 34 pages, 9 figures

The Lorentz-violating isotropic modified Maxwell theory minimally coupled to standard Dirac theory is characterized by a single real dimensionless parameter which is taken to vanish for the case of the standard (Lorentz-invariant) theory. A finite domain of positive and negative values of this Lorentz-violating parameter is determined, in which microcausality and unitarity hold. The main focus of this article is on isotropic modified Maxwell theory, but similar results for two anisotropic nonbirefringent cases are presented in the appendices., Comment: 22 pages; v5: published version

A Lorentz-noninvariant modification of quantum electrodynamics (QED) is considered, which has photons described by the nonbirefringent sector of modified Maxwell theory and electrons described by the standard Dirac theory. These photons and electrons are taken to propagate and interact in a Schwarzschild spacetime background. For appropriate Lorentz-violating parameters, the photons have an effective horizon lying outside the Schwarzschild horizon. A particular type of Compton scattering event, taking place between these two horizons (in the photonic ergoregion) and ultimately decreasing the mass of the black hole, is found to have a nonzero probability. These events perhaps allow for a violation of the generalized second law of thermodynamics in the Lorentz-noninvariant theory considered., Comment: 14 pages; v4: published version in one-column style and with expanded references

There is a unique Lorentz-violating modification of the Maxwell theory of photons, which maintains gauge invariance, CPT, and renormalizability. Restricting the modified-Maxwell theory to the isotropic sector and adding a standard spin-one-half Dirac particle p^\pm with minimal coupling to the nonstandard photon \widetilde{\gamma}, the resulting modified-quantum-electrodynamics model involves a single dimensionless "deformation parameter," \widetilde{\kappa}_{tr}. The exact tree-level decay rates for two processes have been calculated: vacuum Cherenkov radiation p^\pm \to p^\pm \widetilde{\gamma} for the case of positive \widetilde{\kappa}_{tr} and photon decay \widetilde{\gamma} \to p^+ p^- for the case of negative \widetilde{\kappa}_{tr}. From the inferred absence of these decays for a particular high-quality ultrahigh-energy-cosmic-ray event detected at the Pierre Auger Observatory and an excess of TeV gamma-ray events observed by the High Energy Stereoscopic System telescopes, a two-sided bound on \widetilde{\kappa}_{tr} is obtained, which improves by eight orders of magnitude upon the best direct laboratory bound. The implications of this result are briefly discussed., Comment: 18 pages, v5: published version in preprint style

We report on the first observation of a pronounced re-entrant superconductivity phenomenon in superconductor/ferromagnetic layered systems. The results were obtained using a superconductor/ferromagnetic-alloy bilayer of Nb/Cu(1-x)Ni(x). The superconducting transition temperature T_{c} drops sharply with increasing thickness d_{CuNi} of the ferromagnetic layer, until complete suppression of superconductivity is observed at d_{CuNi}= 4 nm. Increasing the Cu(1-x)Ni(x) layer thickness further, superconductivity reappears at d_{CuNi}=13 nm. Our experiments give evidence for the pairing function oscillations associated with a realization of the quasi-one dimensional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) like state in the ferromagnetic layer., Comment: 3 pages, 3 figures, REVTEX4/twocolumn