From probabilities to wave functions: A derivation of the geometric formulation of quantum theory from information geometry

16th Symmetries in Science

Reginatto, Marcel^1

Physikalisch-Technische Bundesanstalt, Bundesallee 100, Braunschweig

38116, Germany^1

关键词: Basic elements;    Geometric formulation;    Geometrical structure;    Hamiltonian formalism;    Information geometry;    Nonlinear gauge transformation;    Symplectic geometry;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/538/1/012018/pdf
DOI  :  10.1088/1742-6596/538/1/012018

来源: IOP

【 摘 要 】

It is shown that the geometry of quantum theory can be derived from geometrical structure that may be considered more fundamental. The basic elements of this reconstruction of quantum theory are the natural metric on the space of probabilities (information geometry), the description of dynamics using a Hamiltonian formalism (symplectic geometry), and requirements of consistency (Kähler geometry). The theory that results is standard quantum mechanics, but in a geometrical formulation that includes also a particular case of a family of nonlinear gauge transformations introduced by Doebner and Goldin. The analysis is carried out for the case of discrete quantum mechanics. The work presented here relies heavily on, and extends, previous work done in collaboration with M. J. W. Hall.