Related papers: Geometry and the Quantum
Following de Broglie and Vigier, a fully relativistic causal interpretation of quantum mechanics is given within the context of a geometric theory of gravitation and electromagnetism. While the geometric model shares the essential…
The fact that quantum theory is non-differentiable, while general relativity is built on the assumption of differentiability sources an incompatibility between quantum theory and gravity. Higher order geometry addresses this issue directly…
A spinfoam model of 3D gravity non-minimally coupled with a scalar field is studied. By discretization of the scalar field, the model is worked out precisely in a purely combinational way. It is shown that the quantum physics of the scalar…
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are the multi-time probability distributions estimated from the results of…
A possible way out of the conundrum of quantum gravity is the proposal that general relativity (GR) is not a fundamental theory but emerges from an underlying microscopic description. Despite recent interest in the emergent gravity program…
It is well known that in quantum gravity, the very geometry of space and time is subject to continual fluctuation. The mathematical formulation for this old theory is still lacking. This article formulates this more than forty-year-old…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
This document contains a description of physics entirely based on a geometric presentation: all of the theory is described giving only a pseudo-riemannian manifold (M, g) of dimension n > 5 for which the g tensor is, in studied domains,…
After a brief introduction, basic ideas of the quantum Riemannian geometry underlying loop quantum gravity are summarized. To illustrate physical ramifications of quantum geometry, the framework is then applied to homogeneous isotropic…
We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent…
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation…
This dissertation explores various nonlinear responses that arise from the rich interplay between quantum geometry, disorder, magnetism and topology in quantum materials. In addition to presenting generalizations of quantum kinetic theory,…
A generalized Noether's theorem and the operational determination of a physical geometry in quantum physics are used to motivate a quantum geometry consisting of relations between quantum states that are defined by a universal group. Making…
I have shown that the field defined by the Wheeler-DeWitt equation for \textit{pure gravity} is neither a standard gravitational field nor the field representing a particular universe. The theory offers a unified description of geometry and…
Based on a clear ontology of material individuals, we analyze in detail the factual semantics of quantum theory, and argue that the basic mathematical formalism of quantum theory is just okay with (a certain form of ) realism and that it is…
We present a geometric formulation of quantum mechanics based on the symplectic structure of the projective Hilbert space. Building upon the standard K\"ahler framework, we introduce an extension in which the symplectic structure is allowed…
In this paper we establish the existence of the non-perturbative theory of quantum gravity known as quantum holonomy theory by showing that a Hilbert space representation of the QHD(M) algebra, which is an algebra generated by…
Caianiello's derivation of Quantum Geometry through an isometric embedding of the spacetime ({\bf M},\tilde{g}) in the pseudo-Riemannian structure ({\bf T^*M},g^*_{AB}) is reconsidered. In the new derivation, a non-linear connection and the…