Topological Field Theory and Quantum Holonomy Representations of Motion Groups

Details Topological Field Theory and Quantum Holonomy Representations of Motion Groups Topological Field Theory and Quantum Holonomy Representations of Motion Groups

1999-08-06

arxiv.org/abs/hep-th/9908051v1

Annals Phys.280:163-208,2000

Physics

High Energy Physics

High Energy Physics - Theory

45 pages LaTeX

Scientific paper

10.1006/aphy.1999.5986

Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological extension of the action and the topological flux quantization conditions, in terms of the Cech cohomology of the underlying spatial manifold, as required for topological invariance of the quantum field theory. The wavefunctions are found in the Hamiltonian formalism and are shown to carry multi-dimensional representations of various topological groups of the space. Expressions for generalized linking numbers in any dimension are thereby derived. In particular, new global aspects of motion group presentations are obtained in any dimension. Applications to quantum exchange statistics of objects in various dimensionalities are also discussed.

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