Classical kinematics and Finsler structures for nonminimal Lorentz-violating fermions

Abstract

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.

26 pages, 5 figures

References in corpus (7)

• Electrodynamics with Lorentz-violating operators of arbitrary dimension
• Planck-scale modified dispersion relations and Finsler geometry
• Riemann-Finsler geometry and Lorentz-violating kinematics
• Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry
• Bipartite Riemann-Finsler geometry and Lorentz violation
• Classical kinematics for Lorentz violation
• The Finsler Type of Space-time Realization of Deformed Very Special Relativity

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• Extended Hamiltonian Formalism and Lorentz-Violating Lagrangians
• Lorentz and CPT tests with charge-to-mass ratio comparisons in Penning traps
• Classical Lagrangians for the nonminimal Standard-Model Extension at higher orders in Lorentz violation
• Finsler Geometries from Topological Electromagnetism
• On axiomatic formulation of gravity and matter field theories with MDRs and Finsler-Lagrange-Hamilton geometry on (co)tangent Lorentz bundles