1994/05/31 by M. Bauer, Michel Bauer, Daniel Z. Freedman +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Quantum and Classical Electrodynamics #Relativity and Gravitational Theory #hep-th
paper · pdf · doi:10.1016/0550-3213(94)90196-1
published as Nucl.Phys.B428:147-168,1994 · 16pp., REVTeX, CERN-TH.7238/94 (Some revision on Secs.3 and 5; one reference added)
arxiv created 1994/06/29 · openalex publication_date 1994/10/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A unitary transformation \Ps [E]=exp (iØ[E]/g) F[E] is used to simplify the Gauss law constraint of non-abelian gauge theories in the electric field representation. This leads to an unexpected geometrization because øai≡ -\dØ[E]/\d Eai transforms as a (composite) connection. The geometric information in øai is transferred to a gauge invariant spatial connection \Gijk and torsion by a suitable choice of basis vectors for the adjoint representation which are constructed from the electric field Eai. A metric is also constructed from Eai. For gauge group SU(2), the spatial geometry is the standard Riemannian geometry of a 3-manifold, and for SU(3) it is a metric preserving geometry with both conventional and unconventional torsion. The transformed Hamiltonian is local. For a broad class of physical states, it can be expressed entirely in terms of spatial geometric, gauge invariant variables.