Related papers: Geometric Approach to Quantum Theory
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
The standard formalism of quantum mechanics is extended to describe a total system including the reference system (RS), with respect to which the total system is described. The RS is assumed to be able to act as a measuring apparatus, with…
I show how quantum mechanics, like the theory of relativity, can be understood as a 'principle theory' in Einstein's sense, and I use this notion to explore the approach to the problem of interpretation developed in my book Interpreting the…
General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…
Quantum information is about the entanglement of states. To this starting point we add parameters whereby a single state becomes a non-vanishing section of a bundle. We consider through examples the possible entanglement patterns of…
We argue that quantum theory is a low-energy effective theory which emerges from some sub-quantum level theory which is of an undulatory and translocal character. We show the close connection of quantum theory with both gravity and the…
Topos theory has been suggested by D\"oring and Isham as an alternative mathematical structure with which to formulate physical theories. In particular, the topos approach suggests a radical new way of thinking about what a theory of…
We consider a quantum theory based on a Galois field. In this approach infinities cannot exist, the cosmological constant problem does not arise, and one irreducible representation (IR) of the symmetry algebra splits into independent IRs…
A recent notion in theoretical physics is that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. These facts find strong evidence in string duality…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
Quantum groups and quantum homogeneous spaces - developed by several authors since the 80's - provide a large class of examples of algebras which for many reasons we interpret as `coordinate algebras' over noncommutative spaces. This…
The semi-classical approach to the quantum geometrodynamical model is used for the description of the properties of the universe on extremely small spacetime scales. Quantum theory for a homogeneous, isotropic and closed universe is…
Proposals for nonlinear extenstions of quantum mechanics are discussed. Two different concepts of "mixed state" for any nonlinear version of quantum theory are introduced: (i) >genuine mixture< corresponds to operational "mixing" of…
Motivated by Quantum Bayesianism I give background for a general epistemic approach to quantum mechanics, where complementarity and symmetry are the only essential features. A general definition of a symmetric epistemic setting is…
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.
An affine quantization approach leads to a genuine quantum theory of general relativity by extracting insights from a short list of increasingly more complex, soluble, perturbably nonrenormalizable models.
Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, a…
This study introduces the quantum force wave equation (QFWE) as a general theory of quantum forces, a novel framework that redefines quantum forces as emergent phenomena arising from the interaction between quantum particles and curved…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…