Titlebook: Spectral Action in Noncommutative Geometry; Micha? Eckstein,Bruno Iochum Book 2018 The Author(s) 2018 Spectral triples.Mellin transforms.a

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Analytic Properties of Spectral Functions, the asymptotic expansion of the corresponding heat trace. We utilise the latter to establish the sought asymptotic expansion of the spectral action at large energies. Finally, we ponder the possibility of obtaining convergent, rather than only asymptotic, formulae for this action.

Intractable

Open Problems,ution to each of these stumbling blocks would advance our understanding of the foundations and implications of the Spectral Action Principle. We therefore cordially invite the Reader to contemplate the list below, both from mathematical and physical perspectives.

流逝

Fluctuations of the Spectral Action,the meromorphic structure of the fluctuated zeta function and, for regular spectral triples with simple dimension spectra, we provide a few formulae for the noncommutative integrals. Finally, we sketch the method of operator perturbations.

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拋射物

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Book 2018ld is spelled out in the fifth Chapter. The book concludes with an appendix including some auxiliary tools from geometry and analysis, along with examples of spectral geometries..The book servesboth as a compendium for researchers in the domain of noncommutative geometry and an invitation to mathematical physicists looking for new concepts..

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