English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this thesis, we studied certain mathematical issues related to thecomputation of the Chamseddine--Connes spectral action on some fundamentalnoncommutative spectral triples, such as the noncommutative torus and thequantum 3-sphere SUq(2). We showed in particular that a Diophantine conditionon the deformation matrix of the torus is crucial to obtain the spectral actionwith real structure. We also studied the question of existence of tadpoles(linear terms in the gauge potential of the fluctuation of the metric in thespectral action) for commutative Riemannian geometries, and the construction ofa symbolic global pseudodifferential calculus allowing a generalization of theWeyl--Moyal product on a Schwartz space of rapidly decaying sections on acotangent bundle of a manifold with linearization.

Spectral action in noncommutative geometry and global pseudodifferential calculus