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On Least Action Principles for Discrete Quantum Scales

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7620)

Abstract

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.

Keywords

  • quantum operators
  • scale relativity

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© 2012 Springer-Verlag Berlin Heidelberg

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Dubois, F., Greff, I., Hélie, T. (2012). On Least Action Principles for Discrete Quantum Scales. In: Busemeyer, J.R., Dubois, F., Lambert-Mogiliansky, A., Melucci, M. (eds) Quantum Interaction. QI 2012. Lecture Notes in Computer Science, vol 7620. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35659-9_2

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  • DOI: https://doi.org/10.1007/978-3-642-35659-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35658-2

  • Online ISBN: 978-3-642-35659-9

  • eBook Packages: Computer ScienceComputer Science (R0)