Abstract
We show that quadratic spaces are a fundamental clue to understand the structure of theoretical physics. Classical Physics is embedded within a 5-D flat quadratic space, 3 Space-, one Time- and one Action- like basis manifolds (Lorentz signature 1,4) faithfully providing a Relativistic Theory (START) describing Newtonian, Maxwell, geometrical optics and General Relativity as particular linear and quadratic forms of this (flat) START space. The 5-D space has a quadratic form which maps into the real quadratic form of a (hyperbolic-complex) 4-D space-time dS2 = dS • dS† . Otherwise the understanding of a many electron quantum mechanical (QM) system, with all its QM intricacies, is presented considering the QM “density” as a quadratic form and the QM “wave function” as its corresponding linear form.
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References
J. KELLER, The Foundations of Density Functional Theory and Wave Quantum Mechanics, Rev. Soc. Quim. Mex. 44 (1) 2000, 22–28
J. KELLER, The Theory of the Electron A Theory of Matter from START, From the series: Fundamental Theories of Physics, Kluwer Academic Publishers, Dordrecht, Vol. 115 (2001), e-book http://www.wkap.nl/prod/b/0-7923-6819-3
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J. KELLER, General Relativity as a Symmetry of a Unified Space-Time-Action Geometrical Space, Proceedings of Institute of Mathematics of NAS of Ukraine, 43 (2) also J. KELLER, A Derivation of Quantum Mechanics from START, idem 50, Editors A.G. Nikitin, V.M. Boyko and R.O. Popovych (and I.A. Yehorchenko), Kyiv, Institute of Mathematics, (2002). 557–568 and (2004).811–820, also J. KELLER AND WEINBERGER P., A Formal Definition of Carriers, Advances in Applied Clifford Algebras, 2002, 12 (1), 39–62. http://www.imath.kiev.ua/activities.php
J. KELLER, Unification of Electrodynamics and Gravity from START, Annales de la Fond. Louis de Broglie, 27 (3) (2002) 359. http://www.ensmp.fr/aflb/AFLB-272/aflb272p359.htm
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KELLER, J. (2006). PRINCIPIA GEOMETRICA PHYSICAE. In: SIDHARTH, B., HONSELL, F., DE ANGELIS, A. (eds) Frontiers of Fundamental Physics. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4339-2_23
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DOI: https://doi.org/10.1007/1-4020-4339-2_23
Publisher Name: Springer, Dordrecht
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