The M?bius symmetry of quantum mechanics

7th International Workshop DICE2014 Spacetime – Matter – Quantum Mechanics

物理学;力学

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: Classical limits;    Conventional quantum mechanics;    Cosmic microwave background radiation;    Minkowski metrics;    Mobius transformations;    Quantum trajectories;    Regularisation;    Spatial spaces;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/626/1/012016/pdf
DOI  :  10.1088/1742-6596/626/1/012016

学科分类：力学，机械学

来源: IOP

【 摘 要 】

The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under D-dimensional Mobius transformations with respect to the Euclidean or Minkowski metrics. The invariance under global Mobius transformations implies that spatial space is compact. Furthermore, it implies energy quantisation and undefinability of quantum trajectories without assuming any prior interpretation of the wave function. The approach may be viewed as conventional quantum mechanics with the caveat that spatial space is compact, as dictated by the Möbius symmetry, with the classical limit corresponding to the decompactification limit. Correspondingly, there exists a finite length scale in the formalism and consequently an intrinsic regularisation scheme. Evidence for the compactness of space may exist in the cosmic microwave background radiation.