The symplectic group and classical mechanics.
The symplectic group is the underlying symmetry group for Hamiltonian dynamics. Yet relatively little is commonly known about its properties including its Lie structure and representations. This paper describes and summarizes some of these properties; and, as a first application of symplectic group theory, provides a symplectic classification of all first-order differential equations in an even number of variables.
Dragt
Alex J
AJ
Center for Theoretical Physics, University of Maryland, College Park, Maryland 20742, USA. dragt@physics.umd.edu