The search for a potential function S allowing us to reconstruct a given metric tensor g and a given symmetric covariant tensor T on a manifold ℳ is formulated as the Hamilton-Jacobi problem associated with a canonically defined Lagrangian on T ℳ. The connection between this problem, the geometric structure of the space of pure states of quantum mechanics, and the theory of contrast functions of classical information geometry are outlined.

Hamilton-Jacobi approach to potential functions in information geometry

FELICE, DOMENICO;MANCINI, Stefano;
2017

Abstract

The search for a potential function S allowing us to reconstruct a given metric tensor g and a given symmetric covariant tensor T on a manifold ℳ is formulated as the Hamilton-Jacobi problem associated with a canonically defined Lagrangian on T ℳ. The connection between this problem, the geometric structure of the space of pure states of quantum mechanics, and the theory of contrast functions of classical information geometry are outlined.
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J. Math. Phys., 2017 vol. 58, art. 063506.pdf

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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11581/400697
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