Deformation Quantization and Nambu Mechanics

Details Deformation Quantization and Nambu Mechanics Deformation Quantization and Nambu Mechanics

1996-02-05

arxiv.org/abs/hep-th/9602016v2

Commun.Math.Phys. 183 (1997) 1-22

Physics

High Energy Physics

High Energy Physics - Theory

Plain LaTeX file with AMS Fonts. 25 pages. Minor clarifying additions and stylistic corrections. To be published in CMP

Scientific paper

10.1007/BF02509794

Starting from deformation quantization (star-products), the quantization problem of Nambu Mechanics is investigated. After considering some impossibilities and pushing some analogies with field quantization, a solution to the quantization problem is presented in the novel approach of Zariski quantization of fields (observables, functions, in this case polynomials). This quantization is based on the factorization over ${\Bbb R}$ of polynomials in several real variables. We quantize the infinite-dimensional algebra of fields generated by the polynomials by defining a deformation of this algebra which is Abelian, associative and distributive. This procedure is then adapted to derivatives (needed for the Nambu brackets), which ensures the validity of the Fundamental Identity of Nambu Mechanics also at the quantum level. Our construction is in fact more general than the particular case considered here: it can be utilized for quite general defining identities and for much more general star-products.

Affiliated with

Also associated with

No associations

Rating

Deformation Quantization and Nambu Mechanics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Deformation Quantization and Nambu Mechanics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Deformation Quantization and Nambu Mechanics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-207939