Hamilton_Jacobi meet M?bius

4th Symposium on Prospects in the Physics of Discrete Symmetries

Faraggi, Alon E.^1 ; Matone, Marco^2

Department of Mathematical Sciences, University of Liverpool, Liverpool

L69 7ZL, United Kingdom^1

Dipartimento di Fisica, Universit'a di Padova, Via Marzolo 8, Padova

I-35131, Italy^2

关键词: Cosmic microwave background radiation;    Energy quantization;    Hamilton-Jacobi;    Hamilton-Jacobi formalism;    Minkowski metrics;    Mobius transformations;    Quantum spacetime;    Quantum trajectories;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/631/1/012010/pdf
DOI  :  10.1088/1742-6596/631/1/012010

来源: IOP

【 摘 要 】

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.