Extended Hamiltonian Formalism and Lorentz-Violating Lagrangians

Abstract

A new perspective on the classical mechanical formulation of particle trajectories in lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant Lagrangian and Hamiltonian varieties is constructed. This approach enables calculation of trajectories using hamilton's equations in momentum space and the Euler-Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.

15 pages

References in corpus (11)

• Matter-gravity couplings and Lorentz violation
• Riemann-Finsler geometry and Lorentz-violating kinematics
• Bipartite Riemann-Finsler geometry and Lorentz violation
• Classical kinematics for Lorentz violation
• Laboratory tests of Lorentz and CPT symmetry with muons
• Classical-physics applications for Finsler $b$ space
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• Measuring the Polarization of a Rapidly Precessing Deuteron Beam
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• Velocity in Lorentz-Violating Fermion Theories
• Covariant Quantization of CPT-violating Photons

Cited by in corpus (6)

• Searches for beyond-Riemann gravity
• Searching for CPT Violation with Neutral-Meson Oscillations
• On the analyticity of static solutions of a field equation in Finsler gravity
• Classical Lagrangians for the nonminimal Standard-Model Extension at higher orders in Lorentz violation
• CPT and Lorentz violation en the Photon and $Z$-boson sector
• Lorentz Violation in Finsler Geometry