Related papers: Geometric Approach to Quantum Theory
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
The characterization of physical systems requires a comprehensive understanding of quantum effects. One aspect is a proper quantification of the strength of such quantum phenomena. Here, a general convex ordering of quantum states will be…
We offer a fresh perspective on the relational interpretation of quantum mechanics as a way of thinking about the world described by quantum theory based on quantifiable notions of information. This allows us to provide a definition of a…
The concept of time as used in various applications and interpretations of quantum theory is briefly reviewed.
En nous laissant guider par la notion de champ qui en fait domine toute la physique nous d\'efinissons la nature physique d'un syst\`eme, ses propri\'et\'es et ses \'etats possibles. Nous proposons alors un cadre tr\`es g\'en\'erale…
There is compelling theoretical evidence that quantum physics will change the face of information science. Exciting progress has been made during the last two decades towards the building of a large scale quantum computer. A quantum group…
Candidate microstates of a spherically symmetric geometry are constructed in the group field theory formalism for quantum gravity, for models including both quantum geometric and scalar matter degrees of freedom. The latter are used as a…
Quantum deformations of sets of points of the real and the complexified projective line are constructed. These deformations depend on the deformation parameter q and certain further parameters \lambda_{ij}. The deformations for which the…
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…
This is an introduction to quantum algebra, from a geometric perspective. The classical spaces $X$, such as the Lie groups, homogeneous spaces, or more general manifolds, are described by various algebras $A$, defined over various fields…
Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual foundations for this canvas, and how these can…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
We introduce a simple quantum mechanical justification for the formation of folded mountains. It is very appealing to develop this idea to a theory of {\it Quantum Geophysics}
In this paper, I propose a project of enlisting quantum information science as a source of task-oriented axioms for use in the investigation of operational theories in a general framework capable of encompassing quantum mechanics, classical…
We revisit the topic of two-state quantum systems using Geometric Algebra (GA) in three dimensions $\mathcal G_3$. In this description, both the quantum states and Hermitian operators are written as elements of $\mathcal G_3$. By writing…
This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…
The determination of the quantum state of a single system by protective observation is used to justify operationally a formulation of quantum theory on the quantum state space (projective Hilbert space) $\cal P$. Protective observation is…
The present paper seeks to construct a quantum theory of the cosmological constant in which its presently observed very small value emerges naturally.
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a…
The only evidence we have for a discrete reality comes from quantum measurements; without invoking these measurements, quantum theory describes continuous entities. This seeming contradiction can be resolved via analysis that treats…