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In this chapter weAlmost-commutative manifold analyze the gauge theories corresponding (in the sense of Chap. 7 ) to a special class of noncommutative manifolds, to wit almost-commutative, or AC manifolds. We will see that this class leads to the usual gauge theories in physics. After identifying the gauge group, the gauge fieldsGauge field and the scalar fieldsScalar field, we compute the spectral actionSpectral action that yields the Lagrangian of physical interest.

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Almost-Commutative Manifolds and Gauge Theories

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  • 出版模式：

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  • 发表日期：

    2025年

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  • Walter D. van Suijlekom

摘要

In this chapter weAlmost-commutative manifold analyze the gauge theories corresponding (in the sense of Chap. 7 ) to a special class of noncommutative manifolds, to wit almost-commutative, or AC manifolds. We will see that this class leads to the usual gauge theories in physics. After identifying the gauge group, the gauge fieldsGauge field and the scalar fieldsScalar field, we compute the spectral actionSpectral action that yields the Lagrangian of physical interest.