Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-05-04
Nucl.Phys.B428:147-168,1994
Physics
High Energy Physics
High Energy Physics - Theory
16pp., REVTeX, CERN-TH.7238/94 (Some revision on Secs.3 and 5; one reference added)
Scientific paper
10.1016/0550-3213(94)90196-1
A unitary transformation $\Ps [E]=\exp (i\O [E]/g) F[E]$ 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 $\o^a_i\equiv -\d\O [E]/\d E^{ai}$ transforms as a (composite) connection. The geometric information in $\o^a_i$ 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.
Bauer Marianne
Freedman Daniel Z.
Haagensen Peter E.
No associations
LandOfFree
Spatial Geometry of the Electric Field Representation of Non-Abelian Gauge Theories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Spatial Geometry of the Electric Field Representation of Non-Abelian Gauge Theories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spatial Geometry of the Electric Field Representation of Non-Abelian Gauge Theories will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-389404