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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The spectral eta function for certain families of Dirac operators onnoncommutative $3$-torus is considered and the regularity at zero is proved. Byusing variational techniques, we show that $\eta_{D}(0)$ is a conformalinvariant. By studying the Laurent expansion at zero of $\text{TR} (|D|^{-z})$,the conformal invariance of $\zeta'_{|D|}(0)$ for noncommutative $3$-torus isproved. Finally, for the coupled Dirac operator, a local formula for thevariation $\partial_A\eta_{D+A}(0)$ is derived which is the analogue of the socalled induced Chern-Simons term in quantum field theory literature.

On Certain Spectral Invariants of Dirac Operators on Noncommutative Tori