To Principles of Quantum Theory Construction

Dmitri Yerchuck^1, , Alla Dovlatova² and Andrey Alexandrov²

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

²M.V.Lomonosov Moscow State University, Moscow

Cite this paper:
Dmitri Yerchuck, Alla Dovlatova and Andrey Alexandrov. To Principles of Quantum Theory Construction. International Journal of Physics. 2014; 2(6):181-188. doi: 10.12691/ijp-2-6-1

Abstract

New insight to the principles of the quantum theory construction is given. It is based on the symmetry study of main differential equations of mechanics and electrodynamics. It has been shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered within the frames of the number theory) determine the mathematical nature of the quantities, incoming in given equations. The substantial consequence of the given consideration is the proof of the main postulate of quantum mechanics, that is, the proof of the statement, that to any quantum mechanical quantity can be set up into the correspondence the Hermitian matrix. It is shown, that a non-abelian character of the multiplicative group of the quaternion ring leads to the nonapplicability of the quaternion calculus for the construction of new versions of quantum mechanics directly. The given conclusion seems to be actual, since there is a number of modern publications with the development of the quantum mechanics theory using the quaternions with the standard basis {e, i, j, k}. The correct way for the construction of new versions of quantum mechanics on the quaternion base is discussed in the paper presented. It is realized by means of the representation of the quaternions through the basis of the linear space of complex numbers over the field of real numbers, under the multiplicative group of which the equations of the dynamics of mechanical systems are invariant. At the same time the quaternion calculus is applicable in electrodynamics, at that the new versions of quantum electrodynamics can be constructed by an infinite number of the ways corresponding to an infinite number of the matrix representations of the standard quaternion basis {e, i, j, k}. The given conclusion is the consequence of the high symmetry of Maxwell equations.

Keywords:
symmetry differential equations quantum theory quaternions

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