从广义相对论到原子尺度的标架统一不变式
A Unified Invariant Formulation, by Frames, from General Relativity to the Atomic Scale
摘要：
本文的目的是用框架，即外微分形式的四元组来表述物理学的基本定律。基本算子是Hodge-de Rham Laplacian d*d*+*d*d的修改，其中 * 是双曲星。在这篇文章中，它根据框架进行了修改。修改后的 * 是w.r.任何一种同构。因此，修改后的拉普拉斯是不变的。本文导出的场方程是真空中广义相对论场方程的完全替代。框架场方程产生牛顿（爱因斯坦）引力定律的推导，而无需求助于测地线公设。导出了库仑定律。给出了麦克斯韦方程组的不变形式。然后考虑一阶线性逼近。它被用来导出薛定谔方程（经典的和相对论的）和狄拉克方程的不变形式，所有这些方程都是线性的。定义在四维流形上的场方程的lhs对所有物体都是一样的。因此，它有望为场论奠定基础。粒子间的相互作用必须计算出来。本文的基本方程是由非空空间中的爱因斯坦方程出发的。
英文摘要：
The aim of this article is the formulation of the basic laws of Physics by frames, i.e. quadruples of exterior differential one forms. The basic operator is a modification of the Hodge-de Rham Laplacian d*d*+*d*d, where * is the hyperbolic star. In this article it is modified depending on the frame. The modified * is invariant w.r. to any diffeomorphism. Consequently, the modified Laplavian is invariant. The field equation developed in this article is a complete alternative to the field equation of General Relativity in vacuum. The frame-field equation yields a derivation of Newtonian (Einstein) law of attraction without recourse to the geodesic postulate. Coulomb law is also derived. Invariant formulation of Maxwell equations is exhibited. Then first order linear approximation is considered. It is used to derive invariant formulation of Schroedinger equation (classical and relativistic) and Dirac equation all of which are linear. The lhs of the field equation, defined on a four dimensional manifold, is the same for all bodies. Thus hopefully, it may set the foundation for a field theory. The interaction of the particles has to be worked out. The basic equation of this article is motivated by the Einstein equation in nonempty space.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
