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Geometry of physical systems on quantized spaces

Vida Milani

Department of Mathematics and Statistics, Utah State University, Logan Utah, UT 84322, USA

E-mail Address: vida_milani@yahoo.com

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Seyed M. H. Mansourbeigi

Department of Computer Science, Utah State University, Logan Utah, UT 84322, USA

E-mail Address: smansourbeigi@aggiemail.usu.edu

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Stephen W. Clyde

Department of Computer Science, Utah State University, Logan Utah, UT 84322, USA

E-mail Address: swc@usu.edu

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https://doi.org/10.1142/S0219887817500402Cited by:0 (Source: Crossref)

Abstract

We present a mathematical model for physical systems. A large class of functions is built through the functional quantization method and applied to the geometric study of the model. Quantized equations of motion along the Hamiltonian vector field are built up. It is seen that the procedure in higher dimension carries more physical information. The metric tensor appears to induce an electromagnetic field into the system and the dynamical nature of the electromagnetic field in curved space arises naturally. In the end, an explicit formula for the curvature tensor in the quantized space is given.

Keywords:

AMSC: 81T75, 53D55, 81R60

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