The Möbius symmetry of quantum mechanics

  title={The M{\"o}bius symmetry of quantum mechanics},
  author={Alon E. Faraggi and Marco Matone},
  journal={Journal of Physics: Conference Series},
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… 

Hamilton–Jacobi meet Möbius

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

Novel Perspectives in String Phenomenology

  • A. Faraggi
  • Physics
    Proceedings of Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2019)
  • 2020
String theory is the leading contemporary framework to explore the synthesis of quantum mechanics with gravity. String phenomenology aims to study string theory while maintaining contact with

The cosmological constant from conformal transformations: Möbius invariance and Schwarzian action

The homogeneous Friedman–Lemaî tre-Robertson–Walker (FLRW) cosmology of a free scalar field with vanishing cosmological constant was recently shown to be invariant under the one-dimensional conformal

Action Quantization, Energy Quantization, and Time Parametrization

The additional information within a Hamilton–Jacobi representation of quantum mechanics is extra, in general, to the Schrödinger representation. This additional information specifies the microstate

Generating the cosmological constant from a conformal transformation

The homogeneous Friedman-Lema\^itre-Robertson-Walker (FLRW) cosmology of a free scalar field with vanishing cosmological constant was recently shown to be invariant under the one-dimensional



Equivalence principle, higher-dimensional Möbius group and the hidden antisymmetric tensor of quantum mechanics

We show that the recently formulated equivalence principle (EP) implies a basic cocycle condition both in Euclidean and Minkowski spaces, which holds in any dimension. This condition, that in one


The removal of the peculiar degeneration arising in the classical concepts of rest frame and time parametrization is at the heart of the recently formulated equivalence principle (EP). The latter,

The Equivalence Postulate of Quantum Mechanics: Main Theorems.

We consider the two main theorems in the derivation of the Quantum Hamilton--Jacobi Equation from the Equivalence Postulate (EP) of quantum mechanics. The first one concerns a basic cocycle

Superluminality and the equivalence postulate of quantum mechanics

An interpretation of the recent results reported by the OPERA collaboration is that neutrinos propagation in vacuum exceeds the speed of light. It has been further been suggested that this

Energy quantisation and time parameterisation

We show that if space is compact, then trajectories cannot be defined in the framework of the quantum Hamilton–Jacobi (HJ) equation. The starting point is the simple observation that when the energy

Geometry and the quantum: basics

A bstractMotivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman