Abstract
Phase space is the framework best suited for quantizing superintegrable systems, naturally preserving the symmetry algebras of the respective Hamiltonian invariants. The power and simplicity of the method is fully illustrated through new applications to nonlinear σ-models, specifically for de Sitter N-spheres and chiral models, where the symmetric quantum Hamiltonians amount to compact and elegant expressions. Additional power and elegance is provided by the use of Nambu brackets to incorporate the extra invariants of superintegrable models. Some new classical results are given for these brackets, and their quantization is successfully compared to that of Moyal, validating Nambu's original proposal.
| Original language | English (US) |
|---|---|
| Journal | New Journal of Physics |
| Volume | 4 |
| State | Published - Oct 29 2002 |
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ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
Deformation quantization of superintegrable systems and Nambu mechanics. / Curtright, Thomas; Zachos, Cosmas K.
In: New Journal of Physics, Vol. 4, 29.10.2002.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Deformation quantization of superintegrable systems and Nambu mechanics
AU - Curtright, Thomas
AU - Zachos, Cosmas K.
PY - 2002/10/29
Y1 - 2002/10/29
N2 - Phase space is the framework best suited for quantizing superintegrable systems, naturally preserving the symmetry algebras of the respective Hamiltonian invariants. The power and simplicity of the method is fully illustrated through new applications to nonlinear σ-models, specifically for de Sitter N-spheres and chiral models, where the symmetric quantum Hamiltonians amount to compact and elegant expressions. Additional power and elegance is provided by the use of Nambu brackets to incorporate the extra invariants of superintegrable models. Some new classical results are given for these brackets, and their quantization is successfully compared to that of Moyal, validating Nambu's original proposal.
AB - Phase space is the framework best suited for quantizing superintegrable systems, naturally preserving the symmetry algebras of the respective Hamiltonian invariants. The power and simplicity of the method is fully illustrated through new applications to nonlinear σ-models, specifically for de Sitter N-spheres and chiral models, where the symmetric quantum Hamiltonians amount to compact and elegant expressions. Additional power and elegance is provided by the use of Nambu brackets to incorporate the extra invariants of superintegrable models. Some new classical results are given for these brackets, and their quantization is successfully compared to that of Moyal, validating Nambu's original proposal.
UR - http://www.scopus.com/inward/record.url?scp=3042563882&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=3042563882&partnerID=8YFLogxK
M3 - Article
VL - 4
JO - New Journal of Physics
JF - New Journal of Physics
SN - 1367-2630
ER -