B^F Theory and Flat Spacetimes

Abstract

We propose a reduced constrained Hamiltonian formalism for the exactly soluble $B\wedge F$ theory of flat connections and closed two-forms over manifolds with topology ${\Sigma }^3\times (0,1)$. The reduced phase space variables are the holonomies of a flat connection for loops which form a basis of the first homotopy group ${\pi }_1({\Sigma }^3)$, and elements of the second cohomology group of ${\Sigma }^3$ with value in the Lie algebra $L(G)$. When $G=SO(3,1)$, and if the two-form can be expressed as $B=e\wedge e$, for some vierbein field $e$, then the variables represent a flat spacetime. This is not always possible: We show that the solutions of the theory generally represent spacetimes with ``global torsion''. We describe the dynamical evolution of spacetimes with and without global torsion, and classify the flat spacetimes which admit a locally homogeneous foliation, following Thurston's classification of geometric structures.

21 pp., Mexico Preprint ICN-UNAM-93-12

References in corpus (2)

• A Hamiltonian Formulation of Topological Gravity
• The Modular Group, Operator Ordering, and Time in (2+1)-Dimensional Gravity

Cited by in corpus (4)

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