SU( N ) Quantum Yang–Mills theory in two dimensions: A complete solution

DOI10.1063/1.532146zbMath0891.53058arXivhep-th/9605128OpenAlexW2059144517WikidataQ58879879 ScholiaQ58879879MaRDI QIDQ4378297

Donald Marolf, Abhay Ashtekar, Jerzy Lewandowski, José Mourão, Thomas Thiemann

Publication date: 6 July 1998

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9605128

zbMATH Keywords

Wilson loopsexpectation valuesfunctional integralsspace of gauge equivalent classes of connectionstwo-dimensional Yang-Mills theories

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Yang-Mills and other gauge theories in quantum field theory (81T13) Applications of differential geometry to physics (53Z05) Axiomatic quantum field theory; operator algebras (81T05) Applications of manifolds of mappings to the sciences (58D30) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07)

Related Items (9)

Quantum field theory on curved backgrounds. I: The Euclidean functional integral ⋮ Operator-algebraic construction of gauge theories and Jones' actions of Thompson's groups ⋮ On thermodynamic and ultraviolet stability bounds for bosonic lattice QCD models in Euclidean dimensions d = 2,3,4 ⋮ A new type of loop independence and SU(N) quantum Yang–Mills theory in two dimensions ⋮ A new type of loop independence and SU(N) quantum Yang–Mills theory in two dimensions ⋮ Loop quantum gravity ⋮ Loop quantum gravity ⋮ Calculation of Wilson loops in two-dimensional Yang-Mills theories ⋮ An infinite-dimensional calculus for generalized connections on hypercubic lattices

Cites Work

• Yang-Mills theory on a circle
• Two dimensional Yang-Mills theory via stochastic differential equations
• A construction of two-dimensional quantum chromodynamics
• Two dimensional gauge theories revisited
• Generalized measures in gauge theory
• Some properties of large-\(N\) two-dimensional Yang-Mills theory.
• Quantum gauge theory on compact surfaces
• On the support of the Ashtekar-Lewandowski measure
• Differential geometry on the space of connections via graphs and projective limits
• Twists and Wilson loops in the string theory of two-dimensional QCD
• Strings and two-dimensional QCD for finite \(N\).
• Explicit form of the Haar measure of U(n) and differential operators
• Spatial infinity as a boundary of spacetime
• Projective techniques and functional integration for gauge theories

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