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

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

Research output: Contribution to journalArticle

15 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)5453-5482
Number of pages30
JournalJournal of Mathematical Physics
Volume38
Issue number11
DOIs
StatePublished - Jan 1 1997

Fingerprint

Yang-Mills Theory
Quantum Theory
axioms
Yang-Mills theory
Two Dimensions
topology
Axioms
Euclidean
strokes
preserving
Topology
equivalence
gauge theory
Wilson Loop
Invariant
Yang-Mills
Gauge Group
continuums
Diffeomorphisms
Stroke

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Ashtekar, Abhay ; Lewandowski, Jerzy ; Marolf, Donald ; Mourão, José ; Thiemann, Thomas. / SU(N) Quantum Yang-Mills theory in two dimensions : A complete solution. In: Journal of Mathematical Physics. 1997 ; Vol. 38, No. 11. pp. 5453-5482.
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Ashtekar, A, Lewandowski, J, Marolf, D, Mourão, J & Thiemann, T 1997, 'SU(N) Quantum Yang-Mills theory in two dimensions: A complete solution', Journal of Mathematical Physics, vol. 38, no. 11, pp. 5453-5482. https://doi.org/10.1063/1.532146

SU(N) Quantum Yang-Mills theory in two dimensions : A complete solution. / Ashtekar, Abhay; Lewandowski, Jerzy; Marolf, Donald; Mourão, José; Thiemann, Thomas.

In: Journal of Mathematical Physics, Vol. 38, No. 11, 01.01.1997, p. 5453-5482.

Research output: Contribution to journalArticle

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