Riemann-Finsler Geometry and Lorentz-Violating Scalar Fields

Abstract

The correspondence between Riemann-Finsler geometries and effective field theories with spin-independent Lorentz violation is explored. We obtain the general quadratic action for effective scalar field theories in any spacetime dimension with Lorentz-violating operators of arbitrary mass dimension. Classical relativistic point-particle lagrangians are derived that reproduce the momentum-velocity and dispersion relations of quantum wave packets. The correspondence to Finsler structures is established, and some properties of the resulting Riemann-Finsler spaces are investigated. The results provide support for open conjectures about Riemann-Finsler geometries associated with Lorentz-violating field theories.

arXiv comment9 pages, version published in Physics Letters B

References in corpus (72)

• Lorentz-Violating Extension of the Standard Model
• CPT Violation and the Standard Model
• Data Tables for Lorentz and CPT Violation
• Gravity, Lorentz Violation, and the Standard Model
• Signals for Lorentz Violation in Electrodynamics
• Stability, Causality, and Lorentz and CPT Violation
• CPT, Strings, and Meson Factories
• Electrodynamics with Lorentz-violating operators of arbitrary dimension
• Matter-gravity couplings and Lorentz violation
• Neutrinos with Lorentz-violating operators of arbitrary dimension
• Fermions with Lorentz-violating operators of arbitrary dimension
• Riemann-Finsler geometry and Lorentz-violating kinematics
• Lorentz-Violating Electrostatics and Magnetostatics
• Bipartite Riemann-Finsler geometry and Lorentz violation
• Causal structure and electrodynamics on Finsler spacetimes
• Lorentz-violating spinor electrodynamics and Penning traps
• Classical kinematics for Lorentz violation
• Redefining Spinors in Lorentz-Violating QED
• Exact solution of vacuum field equation in Finsler spacetime
• Observable effects in a class of spherically symmetric static Finsler spacetimes
• Lorentz and CPT Violation in the Higgs Sector
• On the definition and examples of cones and Finsler spacetimes
• Classical-physics applications for Finsler $b$ space
• Defect Structures in Lorentz and CPT Violating Scenarios
• Casimir effects in Lorentz-violating scalar field theory
• Finsler geometry as a model for relativistic gravity
• Renormalization of Scalar and Yukawa Field Theories with Lorentz Violation
• Eliminating the CPT-Odd f Coefficient from the Lorentz-Violating Standard Model Extension
• Finsler-like structures from Lorentz-breaking classical particles
• Light cones in Finsler spacetime
• Lorentz violation in the gravity sector: The t puzzle
• Thermal corrections to the Casimir energy in a Lorentz-breaking scalar field theory
• Classical Lagrangians and Finsler structures for the nonminimal fermion sector of the Standard-Model Extension
• Finsler-Randers Cosmology: dynamical analysis and growth of matter perturbations
• Classical kinematics and Finsler structures for nonminimal Lorentz-violating fermions
• Non-local on-shell field redefinition for the SME
• Berwald spacetimes and very special relativity
• Standard static Finsler spacetimes
• Kinematics and dynamics in a Bipartite-Finsler spacetime
• Eikonal approximation, Finsler structures, and implications for Lorentz-violating photons in weak gravitational fields
• Neutrino oscillations and Lorentz Invariance Violation in a Finslerian Geometrical model
• Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle
• Classical kinematics for isotropic, minimal Lorentz-violating fermion operators
• Finsler-type modification of the Coulomb law
• On Finsler spacetimes with a timelike Killing vector field
• Extended Hamiltonian Formalism and Lorentz-Violating Lagrangians
• Finslerian Ressiner-Nordstrom spacetime
• Covariant electrodynamics in linear media: Optical metric
• Hadronic Lorentz Violation in Chiral Perturbation Theory
• Mass Renormalization in Lorentz-violating Scalar Field Theory
• Lorentz Violation and the Yukawa Potential
• First-order classical Lagrangians for the nonminimal Standard-Model Extension
• An equivalence of Finslerian relativistic theories
• From classical Lagrangians to Hamilton operators in the Standard-Model Extension
• Observers' measurements in premetric electrodynamics I: Time and radar length
• Three-loop field renormalization for scalar field theory with Lorentz violation
• Lorentz-violating effects in the Bose-Einstein condensation of an ideal bosonic gas
• Lorentz and CPT Violation in Scalar-Mediated Potentials
• Mirrors and field sources in a Lorentz-violating scalar field theory
• Geodesic behavior for Finsler metrics of constant positive flag curvature on $S^2$
• Primordial power spectrum of tensor perturbations in Finsler spacetime
• Lorentz Invariance Violation effects on UHECR propagation: a geometrized approach
• Affine sphere spacetimes which satisfy the relativity principle
• Quasi-Stationary Solutions in Gravity Theories with Modified Dispersion Relations and Finsler-Lagrange-Hamilton Geometry
• One-loop renormalization of Lorentz/CPT violating scalar field theory in curved space-time
• Renormalization in a Lorentz-violating model and higher-order operators
• Euclidean Dilaton Black Hole Vortex and Dirac Fermions
• Lorentz-violating scalar Hamiltonian and equivalence principle in a static metric
• Effective potential in Lorentz-breaking field theory models
• Lifshitz field theories, Snyder noncomutative space-time and momentum dependent metric
• On axiomatic formulation of gravity and matter field theories with MDRs and Finsler-Lagrange-Hamilton geometry on (co)tangent Lorentz bundles
• Unconventional minimal subtraction and Callan-Symanzik methods for Lorentz-violating scalar field theories at all loop orders

Cited by in corpus (62)

• Backgrounds in gravitational effective field theory
• Gauge field theories with Lorentz-violating operators of arbitrary dimension
• Finsler spacetime geometry in Physics
• On the definition and examples of cones and Finsler spacetimes
• Vacuum solution within a metric-affine bumblebee gravity
• An exact stationary axisymmetric vacuum solution within a metric--affine bumblebee gravity
• Cosmology of Lorentz fiber-bundle induced scalar-tensor theories
• Gravity with explicit spacetime symmetry breaking and the Standard-Model Extension
• Dynamics in Varying vacuum Finsler-Randers Cosmology
• Gravitational traces of bumblebee gravity in metric-affine formalism
• 3+1 Formulation of the Standard-Model Extension Gravity Sector
• Thermal aspects of interacting quantum gases in Lorentz-violating scenarios
• Radiative corrections and Lorentz violation
• Analysis of birefringence and dispersion effects from spacetime-symmetry breaking in gravitational waves
• Hamiltonian formulation of an effective modified gravity with nondynamical background fields
• Searches for beyond-Riemann gravity
• Schwarzschild-like solutions in Finsler-Randers gravity
• Lorentz Violation and Sagnac Gyroscopes
• Homogeneously Modified Special Relativity (HMSR) -- A new possible way to introduce an isotropic Lorentz Invariance Violation in particle Standard Model
• Lorentz and CPT tests with charge-to-mass ratio comparisons in Penning traps
• Neutrino Oscillations and Lorentz Invariance Violation
• Searching for CPT Violation with Neutral-Meson Oscillations
• Lorentz-violation-induced arrival time delay of astroparticles in Finsler spacetime
• Geodesic motion in Bogoslovsky-Finsler Spacetimes
• Gravitational lensing and shadow by a Schwarzschild-like black hole in metric-affine bumblebee gravity
• Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle
• Classical Lagrangians for the nonminimal Standard-Model Extension at higher orders in Lorentz violation
• A non-perturbative approach to the scalar Casimir effect with Lorentz symmetry violation
• Bipartite-Finsler symmetries
• Implications of $\text{SU}(2{)}_L$ gauge invariance for constraints on Lorentz violation
• Probing low-energy Lorentz violation from high-energy modified dispersion in dipolar Bose-Einstein condensates
• The Lorentz-violating real scalar field at thermal equilibrium
• Mirrors and field sources in a Lorentz-violating scalar field theory
• Predictions of Ultra-High Energy Cosmic Ray Propagation in the Context of Homogeneously Modified Special Relativity
• Dimensional reduction of the electromagnetic sector of the nonminimal Standard-Model-Extension
• Classical Lagrangians for the nonminimal spin-nondegenerate Standard-Model Extension at higher orders in Lorentz violation
• The Einstein-Hilbert-Palatini formalism in Pseudo-Finsler Geometry
• Effects of Lorentz violation in the Bose-Einstein condensation
• Lorentz violating scalar Casimir effect for a $D$-dimensional sphere
• Lorentz and CPT Violation in Partons
• Classical radiation fields for scalar, electromagnetic, and gravitational waves with spacetime-symmetry breaking
• On metric-affine bumblebee model coupled to scalar matter
• Lorentz Violation in Finsler Geometry
• Effects of Lorentz violation in superconductivity
• Quark-sector Lorentz violation in $Z$-boson production
• On Lorentz invariant complex scalar fields
• From Barthel Randers Kropina Geometries to the Accelerating Universe: A Brief Review of Recent Advances in Finslerian Cosmology
• Trajectories of astroparticles in pseudo-Finsler spacetime with the most general modified dispersion
• Revisiting Legendre transformations in Finsler geometry
• Lorentz-violating extension of scalar QED at finite temperature
• Meson scattering in a Lorentz-violating scalar QED at finite temperature
• Metrizability of SO(3)-invariant connections: Riemann versus Finsler
• Asymmetric particle-antiparticle Dirac equation: first quantization
• Lorentz and CPT Tests using Penning Traps
• Single-Particle Quantum Mechanics of the Free Klein-Gordon Equation with Lorentz Violation
• Exact Lorentz-violating $q$-deformed O($N$) universality class
• Characteristic tensors for almost Finsler manifolds
• Harvesting entanglement from the Lorentz-violating quantum field vacuum in a dipolar Bose-Einstein condensate
• Penning-Trap Searches for Lorentz and CPT Violation
• Scalar Casimir effect for a conducting cylinder in a Lorentz violating background
• Relativistic spin precession in homogeneous background fields
• On the pseudo-Riemann's quartics in Finsler's geometry