Classical kinematics and Finsler structures for nonminimal Lorentz-violating fermions

Understand

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.