Far Eastern Mathematical Journal

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On invariant form of the mass conservation law

Gudimenko A. I., Guzev M.A.

2014, issue 1, P. 33-40

Abstract

The theory of fiber bundles is used for representation of the mass conservation law in a form that is invariant under general transformations of the four space-time coordinates. А generalized formulation of the law is proposed on the base of transition to covariant differentiation. Some physical interpretations of the generalized formulation are discussed.

Keywords: conservation laws, Lie derivative, bundles, covariant derivative

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References

[1] S.K. Godunov, E.I. Romenskii, Elementy mekhaniki sploshnykh sred i zakony sokhraneniia, Nauchnaia kniga, Novosibirsk, 1998. [2] S.P. Novikov, I.A. Taimanov, Sovremennye geometricheskie struktury i polia, MTsNMO, M, 2005. [3] M.M. Postnikov, Lektsii po geometrii. Semestr IV. Differentsial'naia geometriia. Ucheb. posobie dlia vuzov, Nauka. Gl. red. fiz.-mat. lit., M, 1988. [4] I. Kol?ar, P. Michor, J. Slov?ak, Natural operations in differential geometry, Springer-Verlag, Berlin, Heidelberg, New York, 1993. [5] R. Darling, Differential Forms and Connections, Cambridge University Press, 1994. [6] R. Palais, The geometrization of physics, National Tsing Hua University, Hsinchu, Taiwan, 1981. [7] D. Saunders, The Geometry of Jet Bundles, Cambridge Univ. Press, Cambridge, 1989. [8] C. Truesdell, R. Toupin, The classical field theories. In Encyclopedia of Physics edited by S. Flugge, Springer-Verlag, Berlin, Gottingen, Heidelberg, 1960. [9] F. Warner, Foundations of Differentiable Manifolds and Lie Groups, Springer, Berlin, 1983. [10] V.L. Berdichevskii, Variatsionnye printsipy mekhaniki sploshnoi sredy, Nauka. Gl. red. fiz.-mat. lit., M, 1983.

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