On Least Action Principles for Discrete Quantum Scales

  • François Dubois
  • Isabelle Greff
  • Thomas Hélie
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7620)


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.


quantum operators scale relativity 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • François Dubois
    • 1
  • Isabelle Greff
    • 2
  • Thomas Hélie
    • 3
  1. 1.Conservatoire National des Arts et MétiersParisFrance
  2. 2.Department of MathematicsUniversity of PauFrance
  3. 3.IRCAMParisFrance

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