非对易量子引力

Noncommutative Quantum Gravity

摘要: 为解决引力场量子化的困难，我们从一个完全不同的途径引入引力相互作用。本文的基础建立在等效原理和测不准原理上。我们发现对惯性系引入测不准原理将会改变几何结构，使几何成为非对易格，这样在广义相对论的意义上出现了引力场。我们由此得到了半经典的引力子。我们讨论了引力子的动力学和量子化，建立了引力子的场方程。从引力子的场方程出发我们推导出了引力子的Green函数，由此得到的Feynman规则可以解决Feynman积分发散困难。

Abstract: To solve the difficulty of quantization in gravitational field, we introduce a very different approach to the theory of gravitational field. This paper is based on the principle of equivalence and the un-certainty principle. We find that introducing the uncertainty principle into the inertial coordinate system will change the geometry of spacetime, and the geometry of the gravitational field has be-come the noncommutative lattices. Then the gravitational field appears in the sense of the general relativity. We obtain the semiclassical graviton. We discuss the dynamics and quantization of the graviton, and obtain the gravitational field equation. We obtain the Green’s function of the graviton by the field equation, and the resulting Feynman rule can solve the difficulty of the Feynman integral divergence.