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Communication Dans Un Congrès Année : 2012

On least action principles for discrete quantum scales

François Dubois
Isabelle Greff
Thomas Hélie

Résumé

We consider variational problems where the velocity depends on a scale. After recalling the fundamental principles that lead to classical and quantum mechanics, we study the dynamics obtained by replacing the velocity by some physical observable at a given scale into the expression of the Lagrangian function. Then, discrete Euler-Lagrange and Hamilton-Jacobi equations are derived for a continuous model that incorporates a real-valued discrete velocity. We also examine the paradigm for complex-valued discrete velocity, inspired by the scale relativity of Nottale. We present also rigorous definitions and preliminary results in this direction.
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Dates et versions

hal-01161311 , version 1 (08-06-2015)

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  • HAL Id : hal-01161311 , version 1

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François Dubois, Isabelle Greff, Thomas Hélie. On least action principles for discrete quantum scales. Quantum Interaction, Jun 2012, Paris, France. pp.1-11. ⟨hal-01161311⟩
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