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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2015, Volume 25, Issue 1, Pages 36–50 (Mi vuu463)  

MATHEMATICS

On the description of physical fields by methods of Clifford algebra and on the oscillations of a metric of small areas of space

V. A. Kurakina, Yu. I. Khanukaevb

a Department of Applied Physics, Moscow Institute of Physics and Technology (State University), Institutskii per., 9, Dolgoprudnyi, Moscow Region, 141700, Russia
b Department of Theoretical Mechanics, Moscow Institute of Physics and Technology (State University), Institutskiy per., 9, Dolgoprudnyi, Moscow Region, 141700, Russia

Abstract: Assigning the Cartesian coordinate system to real space (linear vector space), I. Newton considered it as a container and didn't associate it with any internal structure. Such an approach leads to the phenomenological description of experimentally observed force fields and compels to attribute a source to each force field. Incorrect (but effective in the aspect of static) interpretation of Clifford algebra in the form of analytical geometry which gained universal recognition thanks to Heaviside's efforts is not algebra in its mathematical understanding. A corollary of this fact is, for example, the absence of concept of measure (spin) in classical mechanics that is experimentally observed.
In contrast to such approach, we assign the vector space having Clifford algebra to real space. This allows us to introduce measures connected with concepts of triad and quadruple and permits a joint consideration of a large number of three-dimensional fields. With objects of reality which are designated by terms of charge and dot mass we associate the force fields explicating the results of experiments that formed the basis of quantum mechanics last century. Features of force fields are referred to as features of a metric and permit existence of statically steady formations without any additional postulates.

Keywords: physical fields, space metric, metric oscillation, Clifford algebra.

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UDC: 512.579
MSC: 15A66, 11R52
Received: 13.02.2015

Citation: V. A. Kurakin, Yu. I. Khanukaev, “On the description of physical fields by methods of Clifford algebra and on the oscillations of a metric of small areas of space”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 25:1 (2015), 36–50

Citation in format AMSBIB
\Bibitem{KurKha15}
\by V.~A.~Kurakin, Yu.~I.~Khanukaev
\paper On the description of physical fields by methods of Clifford algebra and on the oscillations of a~metric of small areas of space
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2015
\vol 25
\issue 1
\pages 36--50
\mathnet{http://mi.mathnet.ru/vuu463}
\elib{http://elibrary.ru/item.asp?id=23142049}


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