Problems in the Foundations of Physics pp 31-48 | Cite as

# Galilei-and Lorentz-Invariant Particle Systems and their Conservation Laws

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## Abstract

Newton’s mechanics of point particles has served as a model of physical theory for two centuries. In its usual formulation, the forces considered are two-body forces depending on the mutual separation of the particles at the same time. The third law implies that these forces are derivable from a potential also depending only on this separation, which allows a Lagrangean formulation of the theory. As was gradually recognized during the past century, this particular form of Newtonian mechanics is invariant under a ten-parameter group, the inhomogeneous Galilei group [1], and possesses ten integrals which are algebraic functions of the positions and velocities; one of these corresponds to the conservation of energy, three to the conservation of linear momentum, three to the conservation of angular momentum, and three express the uniform motion of the center of mass.

## Keywords

Variational Principle Lorentz Group Newtonian Mechanic World Line Modern Phys## Preview

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## References

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