arXiv 1602.071912016-02-18gr-qchep-thmath-phmath.MP

统一场论II：引力与Yang-Mills场和Higgs场的相互作用

A unified field theory II: Gravity interacting with a Yang-Mills and Higgs field

Claus Gerhardt

备注：: 28 p.

摘要：

本文用正则量子化方法研究了引力与杨-米尔斯场和希格斯场的相互作用。类似的方法，在以前的文件中，我们放弃了惠勒-德威特方程和汉密尔顿约束表示的演化方程的平均曲率的超曲面的叶理定义的汉密尔顿设置。在泊松括号的帮助下表示平均曲率的时间导数，这个方程的正则量子化导致$Q=(0,\infty)\times \cal{S}_o$中的波动方程，其中$\cal{S}_o$是Hamilton设置中的柯西超曲面之一。波动方程描述了$\cal{S}_o$中任意黎曼度规与给定的杨-米尔斯场和希格斯场的相互作用。如果度量是完备的，则$Q$是全局双曲的。如果$\cal{S}_o$是紧凑的，我们也证明了一个频谱分辨率的波动方程，并建立了保证质量间隙的充分条件。

英文摘要：

We quantize the interaction of gravity with a Yang-Mills and Higgs field using canonical quantization. Similar to the approach in a previous paper we discard the Wheeler-DeWitt equation and express the Hamilton constraint by the evolution equation of the mean curvature of the hypersurfaces in the foliation defined by the Hamiltonian setting. Expressing the time derivative of the mean curvature with the help of the Poisson brackets the canonical quantization of this equation leads to a wave equation in $Q=(0,\infty)\times \cal{S}_o$, where $\cal{S}_o$ is one of the Cauchy hypersurfaces in the Hamiltonian setting. The wave equation describes the interaction of an arbitrary Riemannian metric in $\cal{S}_o$ and a given Yang-Mills and Higgs field. If the metric is complete $Q$ is globally hyperbolic. In case $\cal{S}_o$ is compact we also prove a spectral resolution of the wave equation and establish sufficient conditions guaranteeing a mass gap.

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。

摘要：

英文摘要：

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