Quantum Equivalent Magnetic Fields that Are Not Classically Equivalent

Carolyn Gordon; William Kirwin; Dorothee Schueth; David Webb

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 $𝒳 \to Δ$ 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 $𝒳 \to S$ 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 $𝒳 \to S$ . We construct a line bundle with connection $(ℒ_{ℱ}, \nabla_{ℱ})$ on $S$ (also in cases when the connection on $ℱ$ has regular singularities). We discuss the resulting $(ℒ_{ℱ}, \nabla_{ℱ})$ mainly in the case $G = ℂ^{*}$ . For instance when $S$ is the moduli space of line bundles with connection over a Riemann surface $X$ , $𝒳 = X \times S$ , and $ℱ$ is the Poincaré bundle over $𝒳$ , we show that $(ℒ_{ℱ}, \nabla_{ℱ})$ provides a prequantization...

Mathematical foundations of geometric quantization.

Arturo Echeverría-Enriquez, Miguel C. Muñoz-Lecanda, Narciso Román-Roy, Carles Victoria-Monge (1998)

Extracta Mathematicae

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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 $\nabla$ and Batchelor model $𝒪_{ℳ} ≅ Γ_{Λ E^{*}}$ . From $(ℳ, \nabla)$ we construct a connection on the total space of the vector bundle $E \to M$ . This reduction of $\nabla$ 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 $\tilde{G}$ is locally homogeneous.

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

Invariance for multiples of the twisted canonical bundle

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

Mathematical foundations of geometric quantization.

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

Invariance of g -natural metrics on linear frame bundles

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

Invariance of $g$ -natural metrics on linear frame bundles