Deformation Quantization of Nambu Mechanics

Details Deformation Quantization of Nambu Mechanics Deformation Quantization of Nambu Mechanics

2003-02-13

arxiv.org/abs/quant-ph/0302106v2

AIP Conf.Proc.672:183-196,2003

Physics

Quantum Physics

Invited talk by the first author at the Coral Gables Conference (C02/12/11.2), Ft Lauderdale, Dec 2002. 14p, LateX2e, aipproc,

Scientific paper

10.1063/1.1594405

Phase Space is the framework best suited for quantizing superintegrable systems--systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of the hamiltonian invariants are preserved most naturally, as illustrated on nonlinear $\sigma$-models, specifically for Chiral Models and de Sitter $N$-spheres. Classically, the dynamics of superintegrable models such as these is automatically also described by Nambu Brackets involving the extra symmetry invariants of them. The phase-space quantization worked out then leads to the quantization of the corresponding Nambu Brackets, validating Nambu's original proposal, despite excessive fears of inconsistency which have arisen over the years. This is a pedagogical talk based on hep-th/0205063 and hep-th/0212267, stressing points of interpretation and care needed in appreciating the consistency of Quantum Nambu Brackets in phase space. For a parallel discussion in Hilbert space, see T Curtright's contribution in these Proceedings [hep-th 0303088].

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