TY - JOUR
T1 - Second order superintegrable systems in conformally flat spaces. III. Three-dimensional classical structure theory
AU - Kalnins, E. G.
AU - Kress, J. M.
AU - Miller, W.
PY - 2005/10
Y1 - 2005/10
N2 - This paper is part of a series that lays the groundwork for a structure and classification theory of second-order superintegrable systems, both classical and quantum, in real or complex conformally flat spaces. Here we consider classical superintegrable systems with nondegenerate potentials in three dimensions. We show that there exists a standard structure for such systems, based on the algebra of 3×3 symmetric matrices, and that the quadratic algebra always closes at order 6. We show that the spaces of truly second-, third-, fourth-, and sixth-order constants of the motion are of dimension 6, 4, 21, and 56, respectively, and we construct explicit bases for the fourth- and sixth order constants in terms of products of the second order constants.
AB - This paper is part of a series that lays the groundwork for a structure and classification theory of second-order superintegrable systems, both classical and quantum, in real or complex conformally flat spaces. Here we consider classical superintegrable systems with nondegenerate potentials in three dimensions. We show that there exists a standard structure for such systems, based on the algebra of 3×3 symmetric matrices, and that the quadratic algebra always closes at order 6. We show that the spaces of truly second-, third-, fourth-, and sixth-order constants of the motion are of dimension 6, 4, 21, and 56, respectively, and we construct explicit bases for the fourth- and sixth order constants in terms of products of the second order constants.
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U2 - 10.1063/1.2037567
DO - 10.1063/1.2037567
M3 - Article
AN - SCOPUS:27844507064
SN - 0022-2488
VL - 46
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
IS - 10
M1 - 103507
ER -