Spectral action in matrix form
Spectral action in matrix form
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DOI：
10.1140/epjc/s10052-020-08618-z
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发表时间：
2020-09
期刊：
影响因子：
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通讯作者：
A. Chamseddine;J. Iliopoulos;Walter D. van Suijlekom
中科院分区：
文献类型：
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作者：
A. Chamseddine;J. Iliopoulos;Walter D. van Suijlekom
迄今为止，非交换几何谱作用的量化是在作用的最终分量形式上进行的，其中所有的迹都在狄拉克矩阵和对称代数上进行。在这项工作中，为了保持形式主义的非交换几何结构，我们导出了矩阵形式的传播子和顶点的量化规则。我们证明了四维欧几里得流形与有限空间乘积的结果，可以用杨-米尔斯理论的形式来表示。我们举例说明了玩具电弱模型的过程。
Quantization of the noncommutative geometric spectral action has so far been performed on the final component form of the action where all traces over the Dirac matrices and symmetry algebra are carried out. In this work, in order to preserve the noncommutative geometric structure of the formalism, we derive the quantization rules for propagators and vertices in matrix form. We show that the results in the case of a product of a four-dimensional Euclidean manifold by a finite space, could be cast in the form of that of a Yang–Mills theory. We illustrate the procedure for the toy electroweak model.