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In the previous chapter we have identified the gauge group canonically associated to any spectral tripleSpectral triple and have derived the generalized gauge fieldsGauge field that carry an action of that gauge group. In this chapter we take the next step and search for gauge invariantsGauge invariant of these gauge fieldsGauge field, to wit, the spectral actionSpectral action, the topological spectralSpectral action actionTopological spectral actionSpectral action and the fermionic actionFermionic action. We derive (asymptotic) expansions of the spectral actionSpectral action.

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Spectral Invariants

  • 章节

  • 出版模式：

    开放获取

  • 发表日期：

    2025年

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  • Walter D. van Suijlekom

摘要

In the previous chapter we have identified the gauge group canonically associated to any spectral tripleSpectral triple and have derived the generalized gauge fieldsGauge field that carry an action of that gauge group. In this chapter we take the next step and search for gauge invariantsGauge invariant of these gauge fieldsGauge field, to wit, the spectral actionSpectral action, the topological spectralSpectral action actionTopological spectral actionSpectral action and the fermionic actionFermionic action. We derive (asymptotic) expansions of the spectral actionSpectral action.