A study of the action from kinematical integral geometry point of view - Del Olmo, M.A.; Santander, M. (Elsevier)
We develop here an interpretation of the classical nonrelativistic and relativistic action for a point particle as related to geometric measures of sets of straight lines (inertial motions) associated in a natural way to closed timelike circuits in space-time. This allows a point of view for the action common to classical and relativistic mechanics. Furthermore the results are not restricted to the free case and also holds for particles in some potentials (homogeneous field and the harmonic oscillator).
http://linkinghub.elsevier.com/retrieve/pii/0393-0440(90)90010-Z
Keywords: SA-SP; U