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

Abstract

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.

63 pages, 4 figures

References in corpus (33)

• Electrodynamics with Lorentz-violating operators of arbitrary dimension
• Signals for Lorentz Violation in Post-Newtonian Gravity
• Matter-gravity couplings and Lorentz violation
• Riemann-Finsler geometry and Lorentz-violating kinematics
• Constraints on Torsion from Lorentz Violation
• Prospects for Large Relativity Violations in Matter-Gravity Couplings
• Vacuum Cerenkov Radiation in Lorentz-Violating Theories Without CPT Violation
• Bipartite Riemann-Finsler geometry and Lorentz violation
• Short-range gravity and Lorentz violation
• Gauge Invariance and the Pauli-Villars Regulator in Lorentz- and CPT-Violating Electrodynamics
• Consistency of isotropic modified Maxwell theory: Microcausality and unitarity
• Classical kinematics for Lorentz violation
• Failure of Gauge Invariance in the Nonperturbative Formulation of Massless Lorentz-Violating QED
• Bounds on length scales of classical spacetime foam models
• One-Loop Renormalization of Pure Yang-Mills with Lorentz Violation
• Classical-physics applications for Finsler $b$ space
• Search for Lorentz violation in short-range gravity
• Time-delay and Doppler tests of the Lorentz symmetry of gravity
• One-Loop Renormalization of the Electroweak Sector with Lorentz Violation
• Feynman propagator for the nonbirefringent CPT-even electrodynamics of the Standard Model Extension
• Lorentz violation in the gravity sector: The t puzzle
• One-Loop Renormalization of QCD with Lorentz Violation
• Quantization and stability of bumblebee electrodynamics
• Classical kinematics and Finsler structures for nonminimal Lorentz-violating fermions
• Lorentz violation and black-hole thermodynamics
• Experimental Design for the LATOR Mission
• Classical kinematics for isotropic, minimal Lorentz-violating fermion operators
• Renormalizability of Yang-Mills theory with Lorentz violation and gluon mass generation
• Eikonal equation of the Lorentz-violating Maxwell theory
• Antimatter, the SME, and Gravity
• Gravitational physics with antimatter
• CPT-odd Photon in Vacuum-Orthogonal Model
• Singular Lorentz-Violating Lagrangians and Associated Finsler Structures

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• Lorentz and CPT Tests with Clock-Comparison Experiments
• Lorentz and CPT Violation in Top-Quark Production and Decay
• Hamiltonian formulation of an effective modified gravity with nondynamical background fields
• Extended Hamiltonian Formalism and Lorentz-Violating Lagrangians
• Lorentz-violating modification of Dirac theory based on spin-nondegenerate operators
• Lorentz and CPT tests with charge-to-mass ratio comparisons in Penning traps
• Anisotropic cubic curvature couplings
• First-order classical Lagrangians for the nonminimal Standard-Model Extension
• Classical Lagrangians for the nonminimal Standard-Model Extension at higher orders in Lorentz violation
• Bipartite-Finsler symmetries
• From classical Lagrangians to Hamilton operators in the Standard-Model Extension
• Fermionic Lorentz violation and its implications for interferometric gravitational-wave detection
• Classical Lagrangians for the nonminimal spin-nondegenerate Standard-Model Extension at higher orders in Lorentz violation
• The Anholonomic Frame and Connection Deformation Method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler-Lagrange-Hamilton theories
• Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos
• Remarks on inverse electrodynamics
• Finslerian geometrodynamics