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Smirnov Rueda, Román (2005) On two complementary types of total time derivative in classical field theories and Maxwell's equations. Foundations of Physics, 35 (10). pp. 16951723. ISSN 00159018

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Official URL: http://link.springer.com/article/10.1007%2Fs1070100565158?LI=true#page1
URL  URL Type 

http://link.springer.com/  Publisher 
http://arxiv.org/abs/physics/0510013  Organisation 
Abstract
Close insight into mathematical and conceptual structure of classical field theories shows serious inconsistencies in their common basis. In other words, we claim in this work to have come across two severe mathematical blunders in the very foundations of theoretical hydrodynamics. One of the defects concerns the traditional treatment of time derivatives in Eulerian hydrodynamic description. The other one resides in the conventional demonstration of the socalled Convection Theorem. Both approaches are thought to be necessary for crossverification of the standard differential form of continuity equation. Any revision of these fundamental results might have important implications for all classical field theories. Rigorous reconsideration of time derivatives in Eulerian description shows that it evokes Minkowski metric for any flow field domain without any previous postulation. Mathematical approach is developed within the framework of congruences for general 4dimensional differentiable manifold and the final result is formulated in form of a theorem. A modified version of the Convection Theorem provides a necessary cross verification for a reconsidered differential form of continuity equation. Although the approach is developed for onecomponent (scalar) flow field, it can be easily generalized to any tensor field. Some possible implications for classical electrodynamics are also explored.
Item Type:  Article 

Additional Information:  The author thanks the referees for their valuable remarks 
Uncontrolled Keywords:  Final Cauchy problem; Continuity equation; Convection theorem; Fluid quantity; Maxwell’s equations. 
Subjects:  Sciences > Physics > Mathematical physics 
ID Code:  20128 
Deposited On:  25 Feb 2013 16:51 
Last Modified:  12 Dec 2018 15:07 
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