Finslerian Isospin--Nonlinear Equations for Pion and Spinor Interactions

Abstract

The Finslerian curvature is introduced in the three-dimensional isospin space, suggesting that the isospin-pion field transforms according to non-linear Finslerian invariance transformations. The fundamental non-linear realization is associated with the pion field triplet. The Finslerian Lagrangian, as well as the implied pion-field selfinteraction, involves the first but no higher derivatives of the pion field. While the invariance transformations are now nonlinear, the conservation laws are still meaningful and sufficient to get the conservations for the energy-momentum and charges. The Finsler-invariant pion-nucleon Lagrangian function is also proposed. The Finslerian isospin-space symmetry is a pure interaction symmetry not shared by the asymptotic fields. The full Klein-Gordon-Dirac equation is accordingly extended. Various details of the implied Finsleroid-structure are formulated in an explicit way.