Poisson brackets of Wilson loops and derivations of free algebras

Journal Article · Thu Feb 01 04:00:00 EST 1996 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531433· OSTI ID:277192

Rajeev, S G; Turgut, O T ^[1]

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1. Department of Physics and Astronomy University of Rochester, Rochester, New York 14627 (United States)

We describe a finite analog of the Poisson algebra of Wilson loops in Yang{endash}Mills theory. It is shown that this algebra arises in an apparently completely different context: as a Lie algebra of vector fields on a noncommutative space. This suggests that noncommutative geometry plays a fundamental role in the manifestly gauge invariant formulation of Yang{endash}Mills theory. We also construct the deformation of the algebra of loops induced by quantization, in the large-{ital N}{sub {ital c}} limit. {copyright} {ital 1996 American Institute of Physics.}

• Research Organization: University of Rochester
• DOE Contract Number: FG02-91ER40685
• OSTI ID: 277192
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 2 Vol. 37; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ALGEBRAS
CONFORMAL INVARIANCE
GAUGE INVARIANCE
LIE GROUPS
PHASE SPACE
QUANTIZATION
VECTOR FIELDS
WILSON LOOP
YANG-MILLS THEORY