516 research outputs found
Spatial Geometry of the Electric Field Representation of Non-Abelian Gauge Theories
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
. A metric is also constructed from . For gauge group ,
the spatial geometry is the standard Riemannian geometry of a 3-manifold, and
for 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.Comment: 16pp., REVTeX, CERN-TH.7238/94 (Some revision on Secs.3 and 5; one
reference added
Reformulating Yang-Mills theory in terms of local gauge invariant variables
An explicit canonical transformation is constructed to relate the physical
subspace of Yang-Mills theory to the phase space of the ADM variables of
general relativity. This maps 3+1 dimensional Yang-Mills theory to local
evolution of metrics on 3 manifolds.Comment: Lattice 2000 (Gravity and Matrix Models) 3 pages, espcrc2.st
Yang--Mills Configurations from 3D Riemann--Cartan Geometry
Recently, the {\it spacelike} part of the Yang--Mills equations has
been identified with geometrical objects of a three--dimensional space of
constant Riemann--Cartan curvature. We give a concise derivation of this
Ashtekar type (``inverse Kaluza--Klein") {\it mapping} by employing a
--decomposition of {\it Clifford algebra}--valued torsion and curvature
two--forms. In the subcase of a mapping to purely axial 3D torsion, the
corresponding Lagrangian consists of the translational and Lorentz {\it
Chern--Simons term} plus cosmological term and is therefore of purely
topological origin.Comment: 14 pages, preprint Cologne-thp-1994-h1
Russia-India relations: the significance of subjective factors
Sergei Lunev argues that Russia should pursue improved political and economic relations with India, despite the many setbacks in the partnership. This is the second of two posts examining parallels and bilateral relations between India and Russia. Click here for a post titled âGlobalisation: Many Indias, many Russiasâ
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