Displaying similar documents to “Quantum Equivalent Magnetic Fields that Are Not Classically Equivalent”

Invariance for multiples of the twisted canonical bundle

Benoît Claudon (2007)

Annales de l’institut Fourier

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Let 𝒳 → Δ a smooth projective family and ( L , h ) a pseudo-effective line bundle on 𝒳 (i.e. with a non-negative curvature current Θ h L ). In its works on invariance of plurigenera, Y.-T. Siu was interested in extending sections of m K 𝒳 0 + L (defined over the central fiber of the family 𝒳 0 ) to sections of m K 𝒳 + L . In this article we consider the following problem: to extend sections of m ( K 𝒳 + L ) . More precisely, we show the following result: assuming the triviality...

Notes on prequantization of moduli of G -bundles with connection on Riemann surfaces

Andres Rodriguez (2004)

Annales mathématiques Blaise Pascal

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Let 𝒳 → S be a smooth proper family of complex curves (i.e. family of Riemann surfaces), and ℱ a G -bundle over 𝒳 with connection along the fibres 𝒳 → S . We construct a line bundle with connection ( ℒ ℱ , ∇ ℱ ) on S (also in cases when the connection on ℱ has regular singularities). We discuss the resulting ( ℒ ℱ , ∇ ℱ ) mainly in the case G = ℂ * . For instance when S is the moduli space of line bundles with connection over a Riemann surface X , 𝒳 = X × S , and ℱ is the Poincaré bundle over 𝒳 , we show that ( ℒ ℱ , ∇ ℱ ) provides a prequantization...

A lossless reduction of geodesics on supermanifolds to non-graded differential geometry

Stéphane Garnier, Matthias Kalus (2014)

Archivum Mathematicum

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Let ℳ = ( M , 𝒪 ℳ ) be a smooth supermanifold with connection ∇ and Batchelor model 𝒪 ℳ ≅ Γ Λ E * . From ( ℳ , ∇ ) we construct a connection on the total space of the vector bundle E → M . This reduction of ∇ is well-defined independently of the isomorphism 𝒪 ℳ ≅ Γ Λ E * . It erases information, but however it turns out that the natural identification of supercurves in ℳ (as maps from ℝ 1 | 1 to ℳ ) with curves in E restricts to a 1 to 1 correspondence on geodesics. This bijection is induced by a natural identification of initial conditions for...

Invariance of g -natural metrics on linear frame bundles

Oldřich Kowalski, Masami Sekizawa (2008)

Archivum Mathematicum

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In this paper we prove that each g -natural metric on a linear frame bundle L M over a Riemannian manifold ( M , g ) is invariant with respect to a lifted map of a (local) isometry of the base manifold. Then we define g -natural metrics on the orthonormal frame bundle O M and we prove the same invariance result as above for O M . Hence we see that, over a space ( M , g ) of constant sectional curvature, the bundle O M with an arbitrary g -natural metric G ˜ is locally homogeneous.