Related papers: Quantized Noncommutative Geometry from Multitrace …
An intersection of Noncommutative Geometry and Loop Quantum Gravity is proposed. Alain Connes' Noncommutative Geometry provides a framework in which the Standard Model of particle physics coupled to general relativity is formulated as a…
The paper is the first of two parts of the work devoted to the investigation of constructing quantum theory of a closed universe as a system without asynptotic states. In Part I the role of asymptotic states in quantum theory of gravity is…
The relativistic quantum phase space (QPS) formalism extends classical phase space by incorporating both mean values and variance-covariance matrices of quantum states, thereby providing a unified setting where the uncertainty principle and…
These notes provide an introduction to the noncommutative matrix geometry which arises within matrix models of Yang-Mills type. Starting from basic examples of compact fuzzy spaces, a general notion of embedded noncommutative spaces…
We consider non minimal coupling between matters and gravity in modified theories of gravity. In contrary to the current common sense, we report that quantum mechanics can effectively emerge when the space-time geometry is sufficiently…
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…
Close to the Planck energy scale, the quantum nature of space-time reveals itself and all forces, including gravity, should be unified so that all interactions correspond to just one underlying symmetry. In the absence of a full quantum…
A general noncommutative-geometric theory of principal bundles is presented. Quantum groups play the role of structure groups. General quantum spaces play the role of base manifolds. A differential calculus on quantum principal bundles is…
A non-perturbative and background-independent quantum formulation of quadratic gravity is provided. A canonical quantization procedure introduced in previous works, named after Dirac and Pauli, is here applied to quadratic gravity to…
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…
Divided into three parts, the first marks out enormous geometric issues with the notion of quasi-freenss of an algebra and seeks to replace this notion of formal smoothness with an approximation by means of a minimal unital commutative…
This paper proposes a method of unifying quantum mechanics and gravity based on quantum computation. In this theory, fundamental processes are described in terms of pairwise interactions between quantum degrees of freedom. The geometry of…
The physical phase space in gauge systems is studied. Effects caused by a non-Euclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac…
We present a path integral formalism for quantising gravity in the form of the spectral action. Our basic principle is to sum over all Dirac operators. The approach is demonstrated on two simple finite noncommutative geometries: the…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
We feel that non-commutative geometry is to particle physics what Riemannian geometry is to gravity. We try to explain this feeling.
In this article, we provide theoretical support for the use of geometric measures of nonclassicality as a general tool to identify quantum phase transitions. We argue that divergences in the susceptibility of any geometric measure of…
Recently Verlinde proposed that gravity can be described as an emergent phenomena arising from changes in the information associated with the positions of material bodies. By using noncommutative geometry as a way to describe the…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
A series of geometric concepts are formulated for $\mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a…