一种引力,电磁和自旋的非对偶统一场论

A Non-Dualistic Unified Field Theory of Gravitation, Electromagnetism and Spin

在Weyl, Eddington, Einstein和Schrdinger概念的框架中,经典统一场论常常不能令人信服,尤其找不到为什么Einstein-Maxwell(E-M)理论需要几何化的任何经验的理由.问题的关键并非是E-M理论是否完美,而是在经典意义下它能否回答现代的所有问题.特别是E-M理论不能提供一个经典理论框架,使Dirac方程能从其中导出,就象Schrdinger方程通过能量方程及对应原理从经典力学中导出一样.本文拟在这个如M.A.Tonnelat所提出的概念框架中,提出一种非对偶的统一场论(UFT).我们将度量式ds^2=g_(μ?)dx^(12)dx^(?)和非退化二次型F=(1/2!)·(?)dx^(?)dx(?)对称地引入理论,得到一种非对偶的统一场论.它包含了Einstein的广义相对论和狭义的Born-Infeld电动力学.尤其重要的是本文指出,采用对应原理,描述在“外部的”引力-电磁场中电子的Dirac方程,可以由非对偶Einstein方程通过简单因式分解导出.

The wisdom of classical unified field theories in the conceptual framework of Weyl, Eddington, Einstein and Schrodinger has often been doubted and in particular there does not appear to be any empirical reason why the Einstein-Maxwell (E-M) theory needs to be geometrized. The crux of the matter is, however, not whether the E-M theory is aesthetically satisfactory but whether it answers all the modern questions within the classical context. In particular, the E-M theory does not provide a classical platform from which the Dirac equation can be derived in the way Schrodinger's equation is derived from classical mechanics via the energy equation and the Correspondence Principle. The present paper presents a non-dualistic unified field theory (UFT) in the said conceptual framework as propounded by M. A. Ton-nelat. By allowing the metric form ds2=gμydxμdxv and the non-degenerate two-form F=(1/2!)ψvdxμ∧dxv to enter symmetrically into the theory we obtain a UFT which contains Einstein's General Relativity and the Born-Infeld electrodynamics as special cases. Above all, it is shown that the Dirac equation describing the electron in an 'external' gravito-electromagnetic field can be derived from the non-dualistic Einstein equation by a simple factorization if the Correspondence Principle is assumed.