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Hamiltonian BF theory and projected Borromean Rings

It is shown that the canonical formulation of the abelian BF theory in D = 3 allows to obtain topological invariants associated to curves and points in the plane. The method consists on finding the Hamiltonian on-shell of the theory coupled to external sources with support on curves and points in the spatial plane. We explicitly calculate a non-trivial invariant that could be seen as a "projection" of the Milnor's link invariant MU(1; 2; 3), and as such, it measures the entanglement of generalized (or projected) Borromeans Rings in the Euclidean plane.

preprint2011arXivOpen access
Ernesto ContrerasAdalberto DíazLorenzo Leal
math-phmath.MPhep-th
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Ernesto ContrerasAdalberto DíazLorenzo Leal

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