The Möbius symmetry of quantum mechanics
Abstract
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 Ddimensional 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.
 Publication:

Journal of Physics Conference Series
 Pub Date:
 July 2015
 DOI:
 10.1088/17426596/626/1/012016
 arXiv:
 arXiv:1502.04456
 Bibcode:
 2015JPhCS.626a2016F
 Keywords:

 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 16 pages. Talk presented at the DICE 2014 international conference, Castiglioncello, Tuscany, September 1519, 2014