Deformation quantization of superintegrable systems and Nambu mechanics

Thomas Curtright, Cosmas K. Zachos

Research output: Contribution to journalArticle

25 Citations (Scopus)

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 languageEnglish (US)
JournalNew Journal of Physics
Volume4
StatePublished - Oct 29 2002

Fingerprint

brackets
preserving
proposals
algebra
symmetry

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 journalArticle

@article{2cd36fd12a6f47549f0f677f449ae156,
title = "Deformation quantization of superintegrable systems and Nambu mechanics",
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.",
author = "Thomas Curtright and Zachos, {Cosmas K.}",
year = "2002",
month = "10",
day = "29",
language = "English (US)",
volume = "4",
journal = "New Journal of Physics",
issn = "1367-2630",
publisher = "IOP Publishing Ltd.",

}

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 -