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Russia Dolgoprudnyi
Section Mathematics
Title On the description of physical fields by methods of Clifford algebra and on the oscillations of a metric of small areas of space
Author(-s) Kurakin V.A.a, Khanukaev Yu.I.a
Affiliations Moscow Institute of Physics and Technologya
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
UDC 512.579
MSC 15A66, 11R52
DOI 10.20537/vm150105
Received 13 February 2015
Language Russian
Citation Kurakin V.A., Khanukaev Yu.I. On the description of physical fields by methods of Clifford algebra and on the oscillations of a metric of small areas of space, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2015, vol. 25, issue 1, pp. 36-50.
  1. Zhilin P.A. Ratsional'naya mekhanika sploshnykh sred (Rational mechanics of continuous media), Saint-Petersburg: Saint-Petersburg Polytechnic University, 2012, 584 p.
  2. Kurakin V.A., Khanukaev Y.I. On balance of the system of dot charges with potentials, oscillating in a near zone, Investigated in Russia, 2004, vol. 7, pp. 1511-1525 (in Russian).
  3. Kurakin V.A., Khanukaev Y.I. On the potential that explaines the results of experiments lying at the basis of quantum mechanics, X International Conference “Stability and oscillations of nonlinear control systems” (Pyatnitskiy conference), Book of abstracts, Moscow, 2008, pp. 164-166 (in Russian).
  4. Conway A.W. On the application of quaternions to some recent developments of electrical theory, Proc. Roy. Irish Acad., 1911, vol. 29, sec. A, pp. 1-9.
  5. Silberstein L. Quaternionic form of relativity, Philosophical Magazine. Series 6, 1912, vol. 23, no. 137, pp. 790-809.
  6. Rashevskii P.K. Teoriya spinorov (Theory of spinors), Moscow: Librokom, 2012.
  7. Kurakin V.A., Khanukaev Y.I. Fields of quaternions as generalization of Maxwell’s equations, Investigated in Russia, 2009, vol. 12, pp. 1477-1485.
  8. Nikol'skii G.A. Vortex effects of penetrating components of sunlight, Magazine of the St. Petersburg University, 28.11.2005, no. 24-25 (in Russian).
  9. Heaviside O. A gravitational and electromagnetic analogy, part I, The Electrician, 1893, vol. 31, pp. 281-282.
  10. Dyatlov V.L. Polyarizatsionnaya model' dipol'nogo fizicheskogo vakuuma (Polarization model of dipole physical vacuum), Novosibirsk: Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, 1998, 183 p.
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