Fuzzy Physics: A Brief Overview of Noncommutative Geometry in Physics

Dualism QM and GR

10.31219/osf.io/8nzwd ◽

2019 ◽

Author(s):

Vitaly Kuyukov

Keyword(s):

Quantum Mechanics ◽

General Theory ◽

Noncommutative Geometry ◽

Quantum Tunneling ◽

Closed Surface ◽

Theory Of Relativity ◽

General Theory Of Relativity ◽

Surface Integral ◽

Definition Of

Quantum tunneling of noncommutative geometry gives the definition of time in the form of holography, that is, in the form of a closed surface integral. Ultimately, the holography of time shows the dualism between quantum mechanics and the general theory of relativity.

Download Full-text

Missing the point in noncommutative geometry

Synthese ◽

10.1007/s11229-020-02998-1 ◽

2021 ◽

Author(s):

Nick Huggett ◽

Fedele Lizzi ◽

Tushar Menon

Keyword(s):

Scalar Field ◽

Noncommutative Geometry ◽

Smooth Manifold ◽

Operational Definition ◽

Spectral Triple ◽

Fundamental Quantity

AbstractNoncommutative geometries generalize standard smooth geometries, parametrizing the noncommutativity of dimensions with a fundamental quantity with the dimensions of area. The question arises then of whether the concept of a region smaller than the scale—and ultimately the concept of a point—makes sense in such a theory. We argue that it does not, in two interrelated ways. In the context of Connes’ spectral triple approach, we show that arbitrarily small regions are not definable in the formal sense. While in the scalar field Moyal–Weyl approach, we show that they cannot be given an operational definition. We conclude that points do not exist in such geometries. We therefore investigate (a) the metaphysics of such a geometry, and (b) how the appearance of smooth manifold might be recovered as an approximation to a fundamental noncommutative geometry.

Download Full-text

Wormhole Solutions in Symmetric Teleparallel Gravity with Noncommutative Geometry

Symmetry ◽

10.3390/sym13071260 ◽

2021 ◽

Vol 13 (7) ◽

pp. 1260

Author(s):

Zinnat Hassan ◽

Ghulam Mustafa ◽

Pradyumn Kumar Sahoo

Keyword(s):

Linear Model ◽

Noncommutative Geometry ◽

Teleparallel Gravity ◽

Exponential Model ◽

Model Parameter ◽

Exponential Models ◽

Feasible Solutions ◽

The Stability ◽

Tov Equation

This article describes the study of wormhole solutions in f(Q) gravity with noncommutative geometry. Here, we considered two different f(Q) models—a linear model f(Q)=αQ and an exponential model f(Q)=Q−α1−e−Q, where Q is the non-metricity and α is the model parameter. In addition, we discussed the existence of wormhole solutions with the help of the Gaussian and Lorentzian distributions of these linear and exponential models. We investigated the feasible solutions and graphically analyzed the different properties of these models by taking appropriate values for the parameter. Moreover, we used the Tolman–Oppenheimer–Volkov (TOV) equation to check the stability of the wormhole solutions that we obtained. Hence, we found that the wormhole solutions obtained with our models are physically capable and stable.

Download Full-text