Symmetry of Differential Equations and Quantum Theory

2nd International Conference on Mathematical Modeling in Physical Sciences 2013

物理学;数学

Yerchuck, Dmitri^1 ; Dovlatova, Alla^2 ; Alexandrov, Andrey^2

Heat-Mass Transfer Institute, National Academy of Sciences of RB, Brovka Str.15, Minsk, 220072, Belarus^1

M.V.Lomonosov Moscow State University, Moscow, 119899, Russia^2

关键词: EM field;    Hermitian matrices;    Hermitians;    High symmetry;    Symmetry groups;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/490/1/012233/pdf
DOI  :  10.1088/1742-6596/490/1/012233

来源: IOP

【 摘 要 】

The symmetry study of main differential equations of mechanics and electrodynamics has shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered in the frame of the number theory) determine the mathematical nature of the quantities, incoming in given equations. It allowed to proof the main postulate of quantum mechanics, that to any mechanical quantity can be set up into the correspondence the Hermitian matrix by quantization. High symmetry of Maxwell equations allows to show, that to EM-field funcions, incoming in given equations, can be set up into the correspondence the Quaternion (twice-Hermitian) matrices by their quantization.