Yang-Mills fields and Riemannian geometry

1994/08/31 by Peter E. Haagensen, K. Johnson, Kenneth Johnson · 4 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th

paper · pdf · doi:10.1016/0550-3213(94)00464-p

published as Nucl.Phys. B439 (1995) 597-616 · 22 PP., HARVMAC. MINOR TYPOS CORRECTED - FINAL VERSION, TO BE PUBLISHED IN NUCL. PHYS. B

arxiv created 1995/02/10 · openalex publication_date 1995/04/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is possible to define new, gauge invariant variables in the Hilbert space of Yang-Mills theories which manifestly implement Gauss' law on physical states. These variables have furthermore a geometrical meaning, and allow one to uncover further constraints physical states must satisfy. For gauge group SU(2), the underlying geometry is Riemannian and based on the group GL(3). The formalism allows also for the inclusion of static color sources and the extension to gauge groups SU(N>2), both of which are discussed here.

Citations

• Spatial geometry of the electric field representation of non-abelian gauge theories

Cited by

• Reformulations of Yang–Mills theories with space–time tensor fields
• The configuration space of low-dimensional Yang-Mills theories
• Yang-Mills theory in three dimensions as a quantum gravity theory
• Unifying Geometrical Representations of Gauge Theory