Abstract
We reformulate the standard Lagrangian formulation to a reparameterization invariant Lagrangian formulation by means of Finsler and Kawaguchi geometry. In our formulation, various types of symmetries that appear in theories of physics are expressed geometrically by symmetries of the Finsler (Kawaguchi) metric, and the conservation laws of energy momentum arise as a part of the Euler–Lagrange equations. The Euler–Lagrange equations are given geometrically in reparameterization invariant form, and the conserved energy-momentum currents can be obtained more easily than by the conventional Lagrangian formulation. The applications to scalar field, Dirac field, electromagnetic field and general relativity are introduced. In particular, we propose an alternative definition of the energy-momentum current of gravity, which satisfies gauge invariance under on-shell conditions.
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