Kähler quantization of H1(T2,R) is studied. It is shown that this theory corresponds to a fermionic σ model targeting a noncommutative space. By solving the complex-structure moduli independence conditions, the quantum background independent wave function is obtained. We study the transformation of the wave function under modular transformation. It is shown that the transformation rule is characteristic to the operator ordering. Similar results are obtained for Kähler quantization of H2(T2,R)⁠.

Topics
Hamiltonian mechanics, Algebraic topology, Partial differential equations, Riemannian geometry, Representation theory, Complex functions, Field theory, Sigma model, Dirac bracket, Statistical thermodynamics
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© 2007 American Institute of Physics.
2007
American Institute of Physics
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