爱因斯坦方程和薛定谔方程的不变联合标架解法
An invariant joint alternative, by frames, to Einstein and Schroedinger equations
摘要：
Hodge-de Rham Laplacean是波动方程形式的扩展。框架是1-形式的四元组。Hodge-de Rham Laplacean被修改为在框架本身上对其进行建模（而不是在标准框架$dx$上）。这种改进的拉普拉斯算子是不变的。基本方程是：对标架的修正拉普拉斯运算等于源项乘以标架。Kaniel和Itin（Il Nuovo Cimento vol 113 B，N3，1998）分析了稳态和球对称框架（广义相对论）的方程。他们计算了一个封闭的解决方案，其导出的度量是罗森的。这个封闭解与史瓦西解本质上是不同的。然而，它通过了三个经典的实验测试，达到了同样的精度。同样的基本方程也是薛定谔方程的替代方程，其中源项是电磁势。得到了与薛定谔方程相同的量子化。建议的系统是双曲的，在对比的时间依赖的薛定谔方程，这是抛物。对于时间相关的帧，方程是相当复杂的。因此，线性化方程被明确地求解。
英文摘要：
The Hodge-de Rham Laplacean is an extension to forms of the wave equation. A frame is a quartuple of 1-forms. The Hodge-de Rham Laplacean is modified to model it on the frame itself (not on the standard frame $dx$). This modified Laplacean is invariant. The basic equation is: The modified Laplacean operating on the frame is equal to a source term times the frame. Kaniel and Itin (Il Nuovo Cimento vol 113B,N3,1998) analyzed the equation for steady state and spherically symmetric frame (General Relativity). They computed a closed solution for which the derived metric is Rosen's. This closed solution is intrinsically different than Schwarzschild solution. Yet it passes the three classical experimental tests to the same accuracy. The same basic equation is,also, the alternative to Schroedinger equation, where the source term is the electromagnetic potential. The same quantization as in Schroedinger equation is attained. The suggested system is hyperbolic, in contrast to the time dependent Schroedinger equation which is parabolic. For time dependent frames the equation is quite complicated. Thus, the linearized equation is explicitly solved .
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