Geometry of Physical Systems on Quantized Spaces
International Journal of Geometric Methods in Modern Physics
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.
"Geometry of Physical Systems", Vida Milani, Seyed M.H. Mansourbeigi and Stephen W. Clyde, International Journal of Geometric Methods in Modern Physics, vol.14, no.3, (2017).