Abstract
The paper is a continuation of a series papers by the author in which it is shown that the equations of contemporary quantum theory (the Klein-Gordon equation and the Dirac integral equation) can be interpreted as conditions of harmonicity of linear form in the manifoldsV4. In this paper, geometrization of classical and quantum interactions of a physical object is performed for the case of an arbitrary external force field in the manifoldkV4. This manifold is constructed on the same set of surfaces as the manifoldsV4. The equation representing conditions of harmonicity of linear form inkV4 is derived and is analogous to the KleinGordon equation.
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Literature cited
K. B. Korotchenko, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 5, 66–70 (1986); No. 9, 70–74 (1990); No. 10, 76–80 (1990).
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G. De Rham, Differentiable Manifolds: Forms, Currents, Harmonic Forms, Springer-Verlag, New York (1984).
Additional information
Tomsk Polytechnical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 3–6, January, 1993.
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Korotchenko, K.B. Geometrical relationship between the classical and quantum descriptions of arbitrary force interactions. Russ Phys J 36, 1–4 (1993). https://doi.org/10.1007/BF00559245
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DOI: https://doi.org/10.1007/BF00559245