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.

arXiv comment15 pages

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Cited by in corpus (19)

• Backgrounds in gravitational effective field theory
• Gauge field theories with Lorentz-violating operators of arbitrary dimension
• Riemann-Finsler Geometry and Lorentz-Violating Scalar Fields
• Lorentz violation in Dirac and Weyl semimetals
• Lorentz and CPT Tests with Clock-Comparison Experiments
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