A. V. Bobylev, G. Vilasi
Projective Invariance for Classical and Quantum Systems
Preprint series: ESI preprints
PACS: O3.20.+i,03.40.Gc,03.65Fd
Abstract: The Lie Group of projective transformations for different physical
systems is considered. It is shown that many mathematically and
physically relevant equations are projectively invariant.
Classical and quantum systems of particles and their
generalizations to kinetic theory and hydrodynamics are considered
from this new view point. New invariant equations and corresponding
Conservation laws are introduced. The specific role of these transformations and
The potential $U(x)=\frac{\alpha} {|x|^2}$ with $x\in {\cal R}^n$ are
discussed from physical and geometrical points of view. It is shown
that all the considered examples are connected with a system of free
particles.


Keywords: projective transformation, projective invariance, conservation laws