Geometric Calculus is developed for curved-space treatments of General Relativity and comparison is made with the flat-space gauge theory approach by Lasenby, Doran and Gull. Einstein’s Principle of Equivalence is generalized to a gauge principle that provides the foundation for a new formulation of General Relativity as a Gauge Theory of Gravity on a curved spacetime manifold. Geometric Calculus provides mathematical tools that streamline the formulation and simplify calculations. The formalism automatically includes spinors so the Dirac equation is incorporated in a geometrically natural way.

中文翻译：

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具有几何微积分的时空几何

几何微积分是为广义相对论的弯曲空间处理而开发的，并与Lasenby，Doran和Gull的平面空间规范理论方法进行了比较。爱因斯坦的等价原理被推广为量规原理，为广义相对论作为弯曲时空流形上的重力规范理论的新表述奠定了基础。几何微积分提供了数学工具，可简化配方并简化计算。形式主义自动包括旋转子，因此以几何自然方式合并了Dirac方程。