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| Synthesized modern mathematics and physics, the author proposes the approaches to the natural world with math-physical three principles. The first principle is the Lagrange-Hamilton principle
where L is Lagrange function of system and G is transform group, while q is space and t is time and ds2 is the metric of space-time. The second principle is the Newton-Einstein principle
where F is strength of field, Ω is curvature and ω is connection. The third principle is the Gauss- Stokes principle
in which Ω is curvature and ω is connection, while χ is characteristic index and M is manifold on real, complex, quaternion or octonion. The three principles can be applied to physical systems with real, complex, quaternion and octonion phases, which produce respectively Euclid-Newton system, Riemman-Einstein system, Finsler-Yang system and a new one.
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| Keywords:mathematical physics; physical philosophy; Hamilton principle; Noether theorem; Einstein equation; Stokes theorem; Gauss-Bonnet formula; Finsler geometry; Yang-Mills field |
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