论文标题
物质的度量性质
The Metric Nature of Matter
论文作者
论文摘要
我们在量规连接的配置空间上构建度量结构，并表明它自然会为弯曲背景上的非扰动，3+1维扬米尔斯量子量子理论产生候选。公制结构是无限二型bott-dirac运算符，而新兴量子场理论的费米子部门是由构建该操作员的无限二维Clifford代数产生的。 BOTT-DIRAC操作员与$ \ Mathbf {HD}（M）$代数相互作用，该代数是由基础歧管上的拟态 - diffeomorforms产生的非共同代数，即沿载体场沿流量的平行转移。该代数与BOTT-DIRAC操作员相结合编码定量的玻色子和费米子场的规范换向和反通信关系。 Bott-Dirac操作员的广场既生产Yang-Mills Hamilton Operator，又生产Dirac Hamilton操作员以及拓扑扬米尔斯术语，以及高衍生的术语和公制不变性。
We construct a metric structure on a configuration space of gauge connections and show that it naturally produces a candidate for a non-perturbative, 3+1 dimensional Yang-Mills-Dirac quantum field theory on a curved background. The metric structure is an infinite-dimensional Bott-Dirac operator and the fermionic sector of the emerging quantum field theory is generated by the infinite-dimensional Clifford algebra required to construct this operator. The Bott-Dirac operator interacts with the $\mathbf{HD}(M)$ algebra, which is a non-commutative algebra generated by holonomy-diffeomorphisms on the underlying manifold, i.e. parallel-transforms along flows of vector fields. This algebra combined with the Bott-Dirac operator encode the canonical commutation and anti-commutation relations of the quantised bosonic and fermionic fields. The square of the Bott-Dirac operator produces both the Yang-Mills Hamilton operator and the Dirac Hamilton operator as well as a topological Yang-Mills term alongside higher-derivative terms and a metric invariant.
