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Title: A survey of star product geometry.

Abstract

A brief pedagogical survey of the star product is provided, through Groenewold's original construction based on the Weyl correspondence. It is then illustrated how simple Landau orbits in a constant magnetic field, through their Dirac Brackets, define a noncommutative structure since these brackets exponentiate to a star product--a circumstance rarely operative for generic Dirac Brackets. The geometric picture of the star product based on its Fourier representation kernel is utilized in the evaluation of chains of star products. The intuitive appreciation of their associativity and symmetries is thereby enhanced. This construction is compared and contrasted with the remarkable phase space polygon construction of Almeida.

Authors:
Publication Date:
Research Org.:
Argonne National Lab., IL (US)
Sponsoring Org.:
US Department of Energy (US)
OSTI Identifier:
761269
Report Number(s):
ANL-HEP-CP-00-085
TRN: US200222%%1
DOE Contract Number:  
W-31-109-ENG-38
Resource Type:
Conference
Resource Relation:
Conference: NATO Advanced Research Workshop: UIC 2000, Chicago, IL (US), 07/22/2000--07/26/2000; Other Information: PBD: 15 Aug 2000
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EVALUATION; DIRAC COSMOLOGY; LANDAU FLUCTUATIONS; ORBITS; MAGNETIC FIELDS; PHASE SPACE

Citation Formats

Zachos, C. A survey of star product geometry.. United States: N. p., 2000. Web.
Zachos, C. A survey of star product geometry.. United States.
Zachos, C. 2000. "A survey of star product geometry.". United States. https://www.osti.gov/servlets/purl/761269.
@article{osti_761269,
title = {A survey of star product geometry.},
author = {Zachos, C},
abstractNote = {A brief pedagogical survey of the star product is provided, through Groenewold's original construction based on the Weyl correspondence. It is then illustrated how simple Landau orbits in a constant magnetic field, through their Dirac Brackets, define a noncommutative structure since these brackets exponentiate to a star product--a circumstance rarely operative for generic Dirac Brackets. The geometric picture of the star product based on its Fourier representation kernel is utilized in the evaluation of chains of star products. The intuitive appreciation of their associativity and symmetries is thereby enhanced. This construction is compared and contrasted with the remarkable phase space polygon construction of Almeida.},
doi = {},
url = {https://www.osti.gov/biblio/761269}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue Aug 15 00:00:00 EDT 2000},
month = {Tue Aug 15 00:00:00 EDT 2000}
}

Conference:
Other availability
Please see Document Availability for additional information on obtaining the full-text document. Library patrons may search WorldCat to identify libraries that hold this conference proceeding.

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