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arXiv 2008.09356hep-thgr-qcmath-phmath.MP
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物质的度量性质

The Metric Nature of Matter

Johannes Aastrup, Jesper M. Grimstrup

摘要:

我们在规范连接的位形空间上构造了一个度规结构,并表明它自然地产生了一个非微扰的3+1维杨-米尔斯-狄拉克量子场论的候选者.度规结构是一个无限维的Bott-Dirac算子,而新兴的量子场论的费米子部分是由构造这个算子所需的无限维Clifford代数产生的。Bott-Dirac算子与$\mathbf{HD}(M)$代数相互作用,$\mathbf{HD}(M)$代数是一个由基础流形上的完整性-同构生成的非交换代数,即沿着向量场流的并行变换。这个代数结合Bott-Dirac算子编码的规范交换和反交换关系的量子玻色子和费米子领域。Bott-Dirac算子的平方产生了杨-米尔斯哈密顿算子和狄拉克哈密顿算子,以及一个拓扑杨-米尔斯项和一个度量不变量。

英文摘要:

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.

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。

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