Mihaela Manoliu | Searcharxiv

arXiv1996

Abelian Chern-Simons theory

We give a construction of the abelian Chern-Simons gauge theory from the point of view of a 2+1 dimensional topological quantum field theory. The definition of the quantum theory relies on geometric quantization ideas which have been previously explored in connection to the nonabelian Chern-Simons theory [JW,ADW]. We formulate the topological quantum field theory in terms of the category of extended 2- and 3-manifolds introduced by Walker [Wa] and prove that it satisfies the axioms of unitary topological quantum field theories formulated by Atiyah [A1].

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arXiv1996

Quantization of symplectic tori in a real polarization

We apply the geometric quantization method with real polarizations to the quantization of a symplectic torus. By quantizing with half-densities we canonically associate to the symplectic torus a projective Hilbert space and prove that the projective factor is expressible in terms of the Maslov-Kashiwara index. As in the quantization of a linear symplectic space, we have two ways of resolving the projective ambiguity: (i) by introducing a metaplectic structure and using half-forms in the definition of the Hilbert space; (ii) by choosing a 4-fold cover of the Lagrangian Grassmannian of the linear symplectic space covering the torus. We show that the Hilbert space constructed through either of these approaches realizes a unitary representation of the integer metaplectic group.

dg-ga↗