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The Superspace of Geometrodynamics
, 2009
"... Wheeler’s Superspace is the arena in which Geometrodynamics takes place. I review some aspects of its geometrical and topological structure that Wheeler urged us to take seriously in the context of canonical quantum gravity. ..."
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Wheeler’s Superspace is the arena in which Geometrodynamics takes place. I review some aspects of its geometrical and topological structure that Wheeler urged us to take seriously in the context of canonical quantum gravity.
Gauge theory in Riem(M)
, 2008
"... In this paper we restrict our attention to an open subset M ′ of Riem(M) = M, consisting solely of metrics with no global symmetry beyond the identity. Therein we have a natural principal fiber bundle (PFB) structure Diff(M) → M π → M/D in which we input the connection form ω i and try to construc ..."
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In this paper we restrict our attention to an open subset M ′ of Riem(M) = M, consisting solely of metrics with no global symmetry beyond the identity. Therein we have a natural principal fiber bundle (PFB) structure Diff(M) → M π → M/D in which we input the connection form ω i and try to construct elements of gauge theory over the associated bundle M ′ ×ρ F, with F = Γ(E), where we are constrained by elements of the theory to take E as a tensorial bundle over M. In spite of the infinite dimensional setting, we succeed in obtaining YangMills equations for gauge fields in superspace. 1