arXiv subjects

M. Schreck

Publications and source records attributed to M. Schreck.

At least 19 recordsLinked to original sources

arXiv2025

Vacuum Cherenkov radiation for nonminimal dimension-5 Lorentz violation

Vacuum Cherenkov radiation is investigated in the Lorentz-violating Standard-Model Extension for isotropic dim-5 operators $\hat{m}$ and $\hat{a}^{\mu}$ in the fermion sector. Both the kinematics and dynamics of this process are analyzed by analytical and numerical means, leading to its decay and radiated-energy rates as functions of the initial-fermion momentum. We adopt the point of view that vacuum Cherenkov radiation is actually a physical phenomenon expected to occur for a charged, massive fermion in the presence of Lorentz violation, when some additional requirements are satisfied. The absence of this effect in ultrahigh-energy cosmic rays detected on Earth allows us to infer stringent bounds on isotropic dim-5 Lorentz violation in protons, quarks, and electrons.

hep-ph↗

arXiv2025

Cosmic Backgrounds in the Gravitational Standard-Model Extension

We consider background fields within the gravitational sector of the Standard-Model Extension (SME) in a cosmological setting. Our analysis is divided into two parts. The first part addresses the consistency of nondynamical backgrounds in scenarios where diffeomorphism invariance is explicitly broken. Focusing on gravitational systems that admit Killing vector fields and possess a priori symmetries, we demonstrate that potential discrepancies between Riemannian geometry and dynamical equations can be avoided. The second part presents a direct application of various techniques developed by decomposing the modified Einstein equations along normal and tangential directions of the (3+1) decomposition. We show that nondynamical backgrounds can lead to accelerated cosmological expansion without requiring a cosmological constant, thereby opening new avenues for interpreting dark energy.

gr-qc↗

arXiv2023

New Developments in the Hamiltonian Formulation of the Gravitational Standard-Model Extension

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.

gr-qc↗

arXiv2019

Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos

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.

hep-th↗

arXiv2019

Vacuum Cherenkov Radiation for Lorentz-Violating Fermions

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.

hep-ph↗

arXiv2019

Classical Lagrangians for the nonminimal Standard-Model Extension at higher orders in Lorentz violation

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 $\hat{a}_μ$, $\hat{c}_μ$, $\hat{e}$, $\hat{f}$, 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.

hep-th↗

arXiv2017

Vacuum Cherenkov radiation for Lorentz-violating fermions

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 projection of the incoming fermion is assumed to be conserved, and in the second, the spin projection is allowed to flip. The first type of process is shown to be still forbidden for the dimensionful $a$ and $b$ coefficients where there are strong indications that it is energetically disallowed for the $H$ coefficients, as well. However, it is rendered possible for the dimensionless $c$, $d$, $e$, $f$, and $g$ coefficients. For large initial fermion energies, the decay rates for the $c$ and $d$ coefficients were found to grow linearly with momentum and to be linearly suppressed by the smallness of the Lorentz-violating coefficient where for the $e$, $f$, and $g$ coefficients this suppression is even quadratic. The decay rates vanish in the vicinity of the threshold, as expected. The decay including a fermion spin flip plays a role for the spin-nondegenerate operators and it was found to occur for the dimensionful $b$ and $H$ coefficients as well as for the dimensionless $d$ and $g$. The characteristics of this process differ much from the properties of the spin-conserving one, e.g., there is no threshold. Based on experimental data of ultra-high-energy cosmic rays, new constraints on Lorentz violation in the quark sector are obtained from the thresholds.

hep-ph↗

arXiv2017

Vacuum Cherenkov radiation for Lorentz-violating fermions

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.

hep-ph↗

arXiv2017

First-order classical Lagrangians for the nonminimal Standard-Model Extension

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.

hep-th↗

arXiv2017

Fermionic Lorentz violation and its implications for interferometric gravitational-wave detection

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.

gr-qc↗

arXiv2016

Lorentz-violating modification of Dirac theory based on spin-nondegenerate operators

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.

hep-th↗

arXiv2016

Classical Nonminimal Lagrangians and Kinematic Tests of Special Relativity

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.

hep-ph↗

arXiv2015

Classical Lagrangians and Finsler structures for the nonminimal fermion sector of the Standard-Model Extension

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 Gröbner 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.

hep-th↗

arXiv2015

Eikonal approximation, Finsler structures, and implications for Lorentz-violating photons in weak gravitational fields

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.

hep-ph↗

arXiv2015

Classical kinematics for isotropic, minimal Lorentz-violating fermion operators

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.

hep-th↗

arXiv2015

Classical kinematics and Finsler structures for nonminimal Lorentz-violating fermions

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.

hep-th↗

arXiv2014

Quantum field theory based on birefringent modified Maxwell theory

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.

hep-th↗

arXiv2014

Quantum field theoretic properties of Lorentz-violating operators of nonrenormalizable dimension in the fermion sector

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.

hep-th↗