Quantization of superintegrable systems with Nambu-Poisson brackets Yavuz Nutku (nutku@gursey.gov.tr)
Abstracts We point
out that Nambu's construction of alternative brackets for super-integrable
systems can be thought of as Poisson brackets with Casimirs in their kernel.
By introducing privileged coordinates in phase space the Nambu-Poisson
brackets are brought to the form of Heisenberg's equations. We propose
a definition for constructing quantum operators for classical functions
which enables us to turn the Nambu-Poisson commutators into a set of eigenvalue
problems. The requirement of the single valuedness of the eigenfunction
leads to quantization. The example of the harmonic oscillator is used
to illustrate this general procedure for quantizing a class of super-integrable
systems. |