Geometry of Quantum Theory

Veeravalli S. Varadarajan

Michel R. P. Planat, Метод Санига

Jincheng Zhang

Quantum Geometry Probability Theory (QGP) offers a novel approach to understanding and modeling non-standard quantum fields (NSFQ) and their potential applications in quantum information and computation. This paper explores the extension of QGP to high-dimensional geometries, constructing a new model for NSFQ generation and investigating its implications for these fields. We detail the core mechanism of incorporating QGP's probability kernel with the geometric structure of quantum geometry, leveraging the unique properties of quantum geometry to compute potential quantum states. This work aims to establish a robust theoretical foundation for NSFQ research and opens avenues for novel quantum phenomena.

James Thomas Wheeler

Jincheng Zhang

Quantum Adaptive Geometry Field Theory (QAGF) is a novel computational model leveraging quantum entanglement and geometry to simulate and predict nonlinear geometric transformations, offering significant computational power for materials science and quantum information applications. This paper details the core mechanism of QAGF, emphasizing the combined application of quantum entanglement and geometric description to model complex quantum effects. The development of QAGF represents a significant advancement in the field, addressing limitations of existing techniques and promising transformative potential across diverse scientific disciplines.

Marcel Reginatto

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.