22,356 research outputs found
Non-Associativity in the Clifford Bundle on the Parallelizable Torsion 7-Sphere
In this paper we discuss generalized properties of non-associativity in
Clifford bundles on the 7-sphere S7. Novel and prominent properties inherited
from the non-associative structure of the Clifford bundle on S7 are
demonstrated. They naturally lead to general transformations of the spinor
fields on S7 and have dramatic consequences for the associated Kac-Moody
current algebras. All additional properties concerning the non-associative
structure in the Clifford bundle on S7 are considered. We further discuss and
explore their applications.Comment: 16 page
Hamiltonian formulation of general relativity in the teleparallel geometry
We establish the Hamiltonian formulation of the teleparallel equivalent of
general relativity, without fixing the time gauge condition, by rigorously
performing the Legendre transform. The time gauge condition, previously
considered, restricts the teleparallel geometry to the three-dimensional
spacelike hypersurface. Geometrically, the teleparallel geometry is now
extended to the four-dimensional space-time. The resulting Hamiltonian
formulation is different from the standard ADM formulation in many aspects, the
main one being that the dynamics is now governed by the Hamiltonian constraint
H_0 and a set of primary constraints. The vector constraint H_i is derived from
the Hamiltonian constraint. The vanishing of the latter implies the vanishing
of the vector constraint.Comment: 22 pages, Latex file, no figures. The title has been changed. The
complete constraint algebra is presented. The derivation of the vector
constraint from the Hamiltonian constraint is presented with further details.
Version to appear in the PR
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