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1

Quantum Riemannian geometry of phase space and nonassociativity

Beggs E. J., Majid S.

Demonstratio Mathematica

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2017

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Vol. 50, nr 1

83--93

EN

Noncommutative or ‘quantum’ differential geometry has emerged in recent years as a process for quantizing not only a classical space into a noncommutative algebra (as familiar in quantum mechanics) but also differential forms, bundles and Riemannian structures at this level. The data for the algebra quantisation is a classical Poisson bracket while the data for quantum differential forms is a Poisson-compatible connection. We give an introduction to our recent result whereby further classical data such as classical bundles, metrics etc. all become quantised in a canonical ‘functorial’ way at least to 1st order in deformation theory. The theory imposes compatibility conditions between the classical Riemannian and Poisson structures as well as new physics such as typical nonassociativity of the differential structure at 2nd order. We develop in detail the case of CPn where the commutation relations have the canonical form [wi, wj] = iλδij similar to the proposal of Penrose for quantum twistor space. Our work provides a canonical but ultimately nonassociative differential calculus on this algebra and quantises the metric and Levi-Civita connection at lowest order in λ.

2

Orderly Disorder in Modern Physics

Davood S. S.

International Letters of Chemistry, Physics and Astronomy

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2015

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Vol. 48

163--172

EN

Fractal structures in various subjects are taken into consideration. In this article, we study fractal structures in physics which could be found or might be existent. Basically, fractals are important because they CHANGE the most basic ways we analyze and understand physics and experimental data.

3

Implementation of a quantized line element in Klein-Gordon and Dirac fields

Bulathsinghala D. L., Wijewardena Gamalath K. A. I. L

International Letters of Chemistry, Physics and Astronomy

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2015

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Vol. 48

68--86

EN

In this paper an ansatz that the anti-commutation rules hold only as integrated average over time intervals and not at every instant giving rise to a time-discrete form of Klein-Gordon equation is examined. This coarse-grained validation of the anti-commutation rules enables us to show that the relativistic energy-momentum relation holds only over discrete time intervals, fitting well with the timeenergy uncertainty relation. When this time-discrete scheme is applied to four vector notations in relativity, the line-element can be quantized and thereby how the physical attributes associated with time, space and matter can be quantized is sketched. This potentially enables us to discuss the Zeno’s arrow paradox within the classical limit. As the solutions of the Dirac equation can be used to construct solutions to the Klein-Gordon equation, this temporal quantization rule is applied to the Dirac equation and the solutions associated with the Dirac equation under such conditions are interpreted. Finally, the general relativistic effects are introduced to a line-element associated with a particle in relativistic motion and a time quantized line-element associated with gravity is obtained.

4

Is Time Inhomogeneous ?

Sadatian S. D.

International Letters of Chemistry, Physics and Astronomy

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2014

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Vol. 13, iss. 2

155--159

EN

In this article, we discuss probability of inhomogeneous time in high or low energy scale of physics. Consequently, the possibility was investigated of using theories such as varying speed of light (VSL) and fractal mathematics to build a framework within which answers can be found to some of standard cosmological problems and physics theories on the basis of time non-homogeneity.

5

Introduce of Generalized Uncertainty Principle

Sadatian S. D.

International Letters of Chemistry, Physics and Astronomy

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2014

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Vol. 20, iss. 1

10--20

EN

We study and explain the uncertainty principle. We've discussed how to reform the uncertainty principle. In this regards, we have used the mechanisms of noncommutative algebra for obtain a generalized uncertainty principle. Following, Due to modified relationship uncertainty, we consider some application of these relation.