Physical Sciences and Mathematics | Open Access Articles

Quantum Equivalent Magnetic Fields That Are Not Classically Equivalent, Carolyn Gordon, William Kirwin, Dorothee Schueth, David Webb

Dartmouth Scholarship

We construct pairs of compact Kähler-Einstein manifolds (Mi,gi,ωi)(i=1,2) of complex dimension n with the following properties: The canonical line bundle Li=⋀ⁿT∗M_i has Chern class [ω_i/2π], and for each positive integer k the tensor powers L^⊗k₁ and L^⊗k₂ are isospectral for the bundle Laplacian associated with the canonical connection, while M₁ and M₂ – and hence T∗M₁ and T∗M₂ – are not homeomorphic. In the context of geometric quantization, we interpret these examples as magnetic fields which are quantum equivalent but not classically equivalent. Moreover, we construct many …

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Quantum Equivalent Magnetic Fields That Are Not Classically Equivalent, Carolyn Gordon, William Kirwin, Dorothee Schueth, David Webb

Dartmouth Scholarship

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