Abstract
A covariant Lagrangian formalism is put forward with an explicit variation of the proper time in the action functional. This approach conforms with the geometrical interpretation in space-time. A general equation of motion is derived, which is not identical with the Euler-Lagrange equation. Momentum and mass are unambiguously defined through the requirement of translational invariance. The rest mass is constant in the special case of electromagnetic field only. A conservation law for the combination of the momentum and the energy momentum-tensor of the free field is derived. No satisfactory Hamiltonian formalism can be established within the framework of the formalism.
- Received 28 April 1960
DOI:https://doi.org/10.1103/PhysRev.123.384
©1961 American Physical Society