Statistics – Applications
Scientific paper
Apr 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003aps..aprc14001w&link_type=abstract
American Physical Society, April Meeting, 2003, April 5-8, 2003 Philadelphia, Pennsylvania, MEETING ID: APR03, abstract #C14.001
Statistics
Applications
Scientific paper
As part of a review paper [Rev. Mod. Phys. 36, 938 (1964)], the second author introduced 4-d Galilei-invariant classical mechanics. Here, we exhibit the calculated two-body invariants from 4-d explicitly tensorial expressions. Newton's second law is generalized to non-instantaneous two-body forces that depend on the 4-positions and -velocities of the particles. In the non-equivalent 4-d Lagrangian case, the two-body forces are generalized to follow from a variational principle using a Green's function that could depend on all the invariants. The very special case of Lagrangian equations of motion for a retarded (or advanced) Green's function is shown to have a Newtonian-like initial value problem by calculating the vanishing of all terms involving integrals over world lines in the usual ten multiple-time conserved quantities. Three Lagrange examples with retarded Green's functions are exhibited. We connect the Lagrangian Galilei-invariant formalism to a fast motion approximation of general relativity theory and suggest possible astrophysical applications.
Havas Peter
Woodcock Harry
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