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arXiv · hep-th/9405028

Spatial Geometry of the Electric Field Representation of Non-Abelian Gauge Theories

M. Bauer·D. Z. Freedman·P. E. Haagensen
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Abstract

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 $ø^a_i\equiv -\dØ[E]/\d E^{ai}$ transforms as a (composite) connection. The geometric information in $ø^a_i$ is transferred to a gauge invariant spatial connection $\G^i_{jk}$ and torsion by a suitable choice of basis vectors for the adjoint representation which are constructed from the electric field $E^{ai}$. A metric is also constructed from $E^{ai}$. 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.

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M. Bauer, D. Z. Freedman, P. E. Haagensen. 1994-06-29. Spatial Geometry of the Electric Field Representation of Non-Abelian Gauge Theories. https://doi.org/10.1016/0550-3213(94)90196-1

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