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

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

doi:10.1063/1.532146

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

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

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18 Scopus citations

Abstract

A closed expression of the Euclidean Wilson-loop functional is derived for pure Yang-Mills continuum theories with gauge groups SU(N) and U(1) and space-time topologies ℝ¹ × ℝ¹ and ℝ¹ × S¹. (For the U(1) theory, we also consider the S¹ × S¹ topology.) The treatment is rigorous, manifestly gauge invariant, manifestly invariant under area preserving diffeomorphisms and handles all (piecewise analytic) loops in one stroke. Equivalence between the resulting Euclidean theory and and the Hamiltonian framework is then established. Finally, an extension of the Osterwalder-Schrader axioms for gauge theories is proposed. These axioms are satisfied in the present model.

Original language	English (US)
Pages (from-to)	5453-5482
Number of pages	30
Journal	Journal of Mathematical Physics
Volume	38
Issue number	11
DOIs	https://doi.org/10.1063/1.532146
State	Published - Nov 1997

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "A closed expression of the Euclidean Wilson-loop functional is derived for pure Yang-Mills continuum theories with gauge groups SU(N) and U(1) and space-time topologies ℝ1 × ℝ1 and ℝ1 × S1. (For the U(1) theory, we also consider the S1 × S1 topology.) The treatment is rigorous, manifestly gauge invariant, manifestly invariant under area preserving diffeomorphisms and handles all (piecewise analytic) loops in one stroke. Equivalence between the resulting Euclidean theory and and the Hamiltonian framework is then established. Finally, an extension of the Osterwalder-Schrader axioms for gauge theories is proposed. These axioms are satisfied in the present model.",

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AU - Ashtekar, Abhay

AU - Lewandowski, Jerzy

AU - Marolf, Donald

AU - Mourão, José

AU - Thiemann, Thomas

PY - 1997/11

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N2 - A closed expression of the Euclidean Wilson-loop functional is derived for pure Yang-Mills continuum theories with gauge groups SU(N) and U(1) and space-time topologies ℝ1 × ℝ1 and ℝ1 × S1. (For the U(1) theory, we also consider the S1 × S1 topology.) The treatment is rigorous, manifestly gauge invariant, manifestly invariant under area preserving diffeomorphisms and handles all (piecewise analytic) loops in one stroke. Equivalence between the resulting Euclidean theory and and the Hamiltonian framework is then established. Finally, an extension of the Osterwalder-Schrader axioms for gauge theories is proposed. These axioms are satisfied in the present model.

AB - A closed expression of the Euclidean Wilson-loop functional is derived for pure Yang-Mills continuum theories with gauge groups SU(N) and U(1) and space-time topologies ℝ1 × ℝ1 and ℝ1 × S1. (For the U(1) theory, we also consider the S1 × S1 topology.) The treatment is rigorous, manifestly gauge invariant, manifestly invariant under area preserving diffeomorphisms and handles all (piecewise analytic) loops in one stroke. Equivalence between the resulting Euclidean theory and and the Hamiltonian framework is then established. Finally, an extension of the Osterwalder-Schrader axioms for gauge theories is proposed. These axioms are satisfied in the present model.

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

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