Poisson Algebra of Wilson Loops and Derivations of Free Algebras

Abstract

We describe a finite analogue of the Poisson algebra of Wilson loops in Yang-Mills theory. It is shown that this algebra arises in an apparently completely different context; as a Lie algebra of vector fields on a non-commutative space. This suggests that non-commutative geometry plays a fundamental role in the manifestly gauge invariant formulation of Yang-Mills theory. We also construct the deformation of the loop algebra induced by quantization, in the large N_c limit.

20 pages, no special macros necessary

References in corpus (3)

• A renormalization group approach to Hamiltonian light-front field theory
• Quantum Hadrondynamics in Two Dimensions
• Poisson Algebra of Wilson Loops in Four-Dimensional Yang-Mills Theory

Cited by in corpus (12)

• The Dilatation Operator of $\mathcal{N}$ $=$ 4 SYM and Classical Limits of Spin Chains and Matrix Models
• Extraction of parton distributions from lattice QCD
• A Lie Algebra for Closed Strings, Spin Chains and Gauge Theories
• Integrable Lambda Models And Chern-Simons Theories
• Symmetries of Large N Matrix Models for Closed Strings
• Symmetry Algebras of Large-N Matrix Models for Open Strings
• Multi-matrix loop equations: algebraic & differential structures and an approximation based on deformation quantization
• A Cohomological Interpretation of the Migdal-Makeenko Equations
• Phase transition in matrix model with logarithmic action: Toy-model for gluons in baryons
• Poisson Brackets of Normal-Ordered Wilson Loops
• Schwinger-Dyson operators as invariant vector fields on a matrix-model analogue of the group of loops
• 2+1 Abelian `Gauge Theory' Inspired by Ideal Hydrodynamics