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. © 2012 Springer-Verlag.
CITATION STYLE
Dubois, F., Greff, I., & Hélie, T. (2012). On least action principles for discrete quantum scales. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7620 LNCS, pp. 13–23). https://doi.org/10.1007/978-3-642-35659-9_2
Mendeley helps you to discover research relevant for your work.