Related papers: Geometrization of Quantum Mechanics
Following the B. Hiley belief that unresolved problems of conventional quantum mechanics could be the result of a wrong mathematical structure, an alternative basic structure is suggested. Critical part of the structure is modification of…
Geometries with horizons offer insights into relationships between general relativity and quantum physics. Quantum mechanics constrains relationships between kinematic parameters and the coordinates describing the dynamics. Example quantum…
A formulation of quantum mechanics based on replacing the general unitary group by finite groups is considered. To solve problems arising in the context of this formulation, we use computer algebra and computational group theory methods.
The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…
An alternative model to describe the electronic and thermal properties of quantum dot based on triangle geometry is proposed. The model predicts characteristics and limitations of the system by controlling the magnetic field and…
We construct a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective…
The review is devoted to topological global aspects of quantal description. The treatment concentrates on quantizations of kinematical observables --- generalized positions and momenta. A broad class of quantum kinematics is rigorously…
The geometry of the Quantum State Space, described by Bloch vectors, is a very intricate one. A deeper understanding of this geometry could lead to the solution of some difficult problems in Quantum Foundations and Quantum Information such…
We present a geometrical description of the space of density states of a quantum system of finite dimension. After presenting a brief summary of the geometrical formulation of Quantum Mechanics, we proceed to describe the space of density…
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of…
Starting from the groupoid approach to Schwinger's picture of Quantum Mechanics, a proposal for the description of symmetries in this framework is advanced.It is shown that, given a groupoid $G\rightrightarrows \Omega$ associated with a…
Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing…
The phenomenon of quantum entanglement is thoroughly investigated, focussing especially on geometrical aspects and on bipartite systems. After introducing the formalism and discussing general aspects, some of the most important separability…
It is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying instead solely on the density matrix as the description of reality. With this definition of a physical…
Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized "step" represents a distinct topological state. Here, we seek a counterpart for "visualizing" quantum geometry, which is a broader…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
The usual quantization of a classical space-time field does not touch the non-geometrical character of quantum mechanics. We believe that the deep problems of unification of general relativity and quantum mechanics are rooted in this poor…
Extended Schwinger's quantization procedure is used for constructing quantum mechanics on a manifold with a group structure. The considered manifold $M$ is a homogeneous Riemannian space with the given action of isometry transformation…
The shape space of k labelled points on a plane can be identified with the space of pure quantum states of dimension k-2. Hence, the machinery of quantum mechanics can be applied to the statistical analysis of planar configurations of…
An attempt is made to formulate quantum mechanics (QM) in physical rather than in mathematical terms. It is argued that the appropriate conceptual framework for QM is "contextual objectivity", which includes an objective definition of the…