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Quantum Equivalent Magnetic Fields that Are Not Classically Equivalent

Carolyn GordonWilliam KirwinDorothee SchuethDavid Webb — 2010

Annales de l’institut Fourier

We construct pairs of compact Kähler-Einstein manifolds ( M i , g i , ω i ) ( i = 1 , 2 ) of complex dimension n with the following properties: The canonical line bundle L i = n T * M i has Chern class [ ω i / 2 π ] , and for each positive integer k the tensor powers L 1 k and L 2 k are isospectral for the bundle Laplacian associated with the canonical connection, while M 1 and M 2 – and hence T * M 1 and T * M 2 – are not homeomorphic. In the context of geometric quantization, we interpret these examples as magnetic fields which are quantum equivalent but not classically equivalent....

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