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The Symplectic Group and Classical Mechanics
Author(s) -
DRAGT ALEX J.
Publication year - 2005
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1196/annals.1350.025
Subject(s) - symplectic geometry , symplectic group , symplectic representation , symplectomorphism , group (periodic table) , symmetry group , moment map , mathematics , hamiltonian (control theory) , pure mathematics , hamiltonian mechanics , lie group , mathematical physics , physics , quantum mechanics , geometry , mathematical optimization , phase space
A bstract : 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 firs–‐order differential equations in an even number of variables.