2015/03/04 by Alon E. Faraggi, Marco Matone
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Hamiltonian (control theory) #Mathematical physics #Mathematics #Minkowski space #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantization (signal processing) #Quantum Mechanics and Applications #Quantum mechanics #Theoretical physics #hep-th
paper · pdf · doi:10.1088/1742-6596/631/1/012010
published as J.Phys.Conf.Ser. 631 (2015) no.1, 012010 · 20 pages. Talk presented at the DISCRETE 2014 international conference, King's College, London, 2-6 December 2014
arxiv created 2015/03/04 · openalex publication_date 2015/07/30 · arxiv updated 2018/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Adaptation of the Hamilton–Jacobi formalism to quantum mechanics leads to a cocycle condition, which is invariant under D -dimensional Mobius transformations with Euclidean or Minkowski metrics. In this paper we aim to provide a pedagogical presentation of the proof of the Möbius symmetry underlying the cocycle condition. The Möbius symmetry implies energy quantization and undefinability of quantum trajectories, without assigning any prior interpretation to the wave function. As such, the Hamilton–Jacobi formalism, augmented with the global Möbius symmetry, provides an alternative starting point, to the axiomatic probability interpretation of the wave function, for the formulation of quantum mechanics and the quantum spacetime. The Möbius symmetry can only be implemented consistently if spatial space is compact, and correspondingly if there exist a finite ultraviolet length scale. Evidence for nontrivial space topology may exist in the cosmic microwave background radiation.