Phys. Rev. 123, 384–390 (1961)Lagrangian Formalism in Relativistic DynamicsReceived 28 April 1960; published in the issue dated July 1961 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. © 1961 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRev.123.384
DOI:
10.1103/PhysRev.123.384
PACS:
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