2005/08/31 by E. Gozzi, D. Mauro · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Algebra over a field #Applied mathematics #Artificial intelligence #Computer science #Force Microscopy Techniques and Applications #Generalization #Geometry #Inverse #Mathematical analysis #Mathematics #Physics #Protein Structure and Dynamics #Pure mathematics #Quantum mechanics #Scale (ratio) #Similarity (geometry) #Statistical Mechanics and Entropy #Symmetry (geometry) #Von Neumann architecture #hep-th #quant-ph
paper · pdf · doi:10.1088/0305-4470/39/13/018
published as J.Phys.A39:3411-3424,2006 · 9 pages, Latex, a new section added
arxiv created 2005/09/21 · openalex publication_date 2006/03/15 · arxiv updated 2014/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we study the symmetry known (Landau and Lifshits 1976 Course of Theoretical Physics vol 1: Mechanics (Oxford: Pergamon)) as mechanical similarity (LMS) and present for any monomial potential. We analyse it in the framework of the Koopman–von Neumann formulation of classical mechanics and prove that in this framework the LMS can be given a canonical implementation. We also show that the LMS is a generalization of the scale symmetry which is present only for the inverse square and a few other potentials. Finally, we study the main obstructions which one encounters in implementing the LMS at the quantum-mechanical level.