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Four-force
About: Four-force is a research topic. Over the lifetime, 3459 publications have been published within this topic receiving 87308 citations.
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TL;DR: The covariant ADM formalism for the full Hilbert Lagrangian of general relativity was discussed in this paper, where a general expression for the naturally ensuing surface integrals was given, which suitably generalize the terms introduced by Regge and Teitelboim.
Abstract: The covariant ADM formalism is discussed for the full Hilbert Lagrangian of general relativity. A general expression for the naturally ensuing surface integrals is given, which suitably generalize the terms introduced by Regge and Teitelboim. In particular, this allows us to interpret a surface term which is usually discardeda priori.
23 citations
TL;DR: In this article, the motion of a particle subject to the restoring force exerted by a linear spring was studied under the assumption that the mass depends upon the speed according to the formula given by the theory of special relativity.
Abstract: This is a study of the motions of a particle subject to the restoring force exerted by a linear spring, under the assumption that the mass depends upon the speed according to the formula given by the theory of special relativity
23 citations
TL;DR: In this paper, the authors summarize what is known about the initial-boundary value problem for general relativity and discuss present problems related to it, and present solutions to the problems they identified.
Abstract: In this article we summarize what is known about the initial-boundary value problem for general relativity and discuss present problems related to it.
23 citations
TL;DR: The theory of scale relativity as discussed by the authors generalizes the application domain of Einstein's principle of relativity to scale transformations of space-time resolutions, which implies its fractal character, and the effects of non-differentiability (complex nature of wave function, new terms in differential equations of mean motion) are accounted for by a scale covariant derivative that transforms the equations of classical mechanics into the Schrodinger equation.
Abstract: The theory of scale relativity generalizes the application domain of Einstein's principle of relativity to scale transformations of space-time resolutions. In this theory, we no longer assume that the space-time continuum is differentiable, this implying its fractal character. Both classical and quantum laws may emerge from a unique, more profound, scale law. The effects of nondifferentiability (complex nature of wave function, new terms in differential equations of mean motion) are accounted for by a scale- covariant derivative that transforms the equations of classical mechanics into the Schrodinger equation. Using an intermediate description in terms of a "fractal potential", we finally establish the m -1 dependence of the Compton- de Broglie wavelength. © Elsevier Science Ltd. All rights reserved
23 citations
TL;DR: In this article, the covariant canonical formalisms for minimal surfaces are developed for relativistic string or membrane embeddings, which avoid the difficulties of the Dixac constraint formalism by modifying the very important approach by Bund.
Abstract: We pursue the renewed interest in string or embedding model for general relativity. Our theory is free of the objections raised by Deseret al., because it takes the embedding space seriously as the arena for physics. We consider a classical space-timeV4 as a minimal surface in a curved embedding spaceVN. Matter onV4 comes from the curvature ofVn. Two versions of the covariant canonical formalisms for minimal surfaces are then developed. They avoid the difficulties of the Dixac constraint formalism; this is achieved by properly modifying the very important approach by Bund. Our canonical formalisms can be used also for relativistic strings or membranes.
23 citations